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SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 


'Return To 

SCIENCE AND TECHNOIOBY DIVISION 

Library of Congress 


Manuscript and illustrations for this volume were prepared for 
publication by the Summary Reports Group of the Columbia Uni- 
versity Division of War Research under contract OEMsr-1131 with 
the Office of Scientific Research and Development. This volume was 
printed and bound by the Columbia University Press. 

Distribution of the Summary Technical Report of NDRC has been 
made by the War and Navy Departments. Inquiries concerning the 
availability and distribution of the Summary Technical Report 
volumes and microfilmed and other reference material should be 
addressed to the War Department Library, Room lA-522, The 
Pentagon, Washington 25, D. C., or to the Office of Naval Research, 
Navy Department, Attention: Reports and Documents Section, 
Washington 25, D. C. 


Copy No. 

S 


This volume, like the seventy others of the Summary Technical 
Report of NDRC, has been written, edited, and printed under great 
pressure. Inevitably there are errors which have slipped past Division 
readers and proofreaders. There may be errors of fact not known 
at time of printing. The author has not been able to follow through 
his writing to the final page proof. 

Please report errors to : 

JOINT RESEARCH AND DEVELOPMENT BOAPiD 
PPtOGRAMS DIVISION (STR ERRATA ) 

WASHINGTON 25, D. C. 

A master errata sheet will be compiled from these reports and sent 
to recipients of the volume. A^our help will make this book more 
useful to other readers and will be of great value in preparing any 
revisions. 


SUMMARY TECHNICAL REPORT OF THE 
COMMITTEE ON PROPAGATION, NDRC 

VOLUME 2 


RADIO WAVE PROPAGATION 
EXPERIMENTS 


OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 
VANNEVAR BUSH, DIRECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CONANT, CHAIRMAN 

COMMITTEE ON PROPAGATION 
CHAS. R. BURROWS, CHAIRMAN 


WASHINGTON, D. C., 1946 


NATIONAL DEFENSE RESEARCH COMMITTEE 


James 1>. Coiiaiit, CJiairnian 
Uiehard C. Tolmaii, Vice Chairman 
Tioger Adams Army liepreseiitativc^ 

Frank B. JeM'ett Navy Representative” 

Karl T. Compton Commissioner of Patents^ 

Irvin SteM^art, Execidive Secretary 


^Anny Representatives in order of service: 


Maj. Gen. G. V. Strong 
Maj. Gen. R. C. Moore 


Col. L. A. Denson 
Col. P. R. Faymonville 
Brig. Gen. E. A. Regnier 
Col. M. M. Irvine 


Maj. Gen. C. C. Williams 
Brig. Gen. W. A. Wood, Jr. 

Col. E. A. Routheau 


^Navy Representatives in order of service: 

Rear Adin. H. G. Bowen Rear Adm. J. A. Furer 

Ca])t. Lybrand P. Smith Rear Adm. A. H. Van Keuren 

Commodore H. A. Schade 
^Commissioners of Patents in order of service: 

Conway P. Coe Casper W. Ooms 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
l)rojects and research programs on the instrumentalities of 
warfare, together with contract facilities for carrying out 
these projects and programs, and (2) to administer the tech- 
nical and scientific work of the contracts. More specifically, 
NDRC functioned by initiating research projects on requests 
from the Army or the Navy, or on requests from an allied 
government transmitted through the Liaison Office of OSRD, 
or on its own considered initiative as a result of the experience 
of its members. Proposals prepared by the Division, Panel, or 
Committee for research contracts for performance of the work 
involved in such projects were first reviewed by NDRC, and 
if approved, recommended to the Director of OSRD, Upon 
a})proval of a proposal by the Director, a contract permitting 
maximum flexibility of scientific effort was arranged. The 
business aspects of the contract, including such matters as 
materials, clearances, vouchers, patents, priorities, legal 
matters, and administration of patent matters were handled 
by the Executive Secretary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division A — Armor and Ordnance 

Division B — Bombs, Fuels, Gases, & Chemical Problems 
Division C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
Division E — Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three 
administrative divisions, panels, or committees were created, 
each with a chief selected on the basis of his outstanding work 
in the particular field. The NDRC members then became a 
reviewing and advisory grouj) to the Director of OSRD. The 
final organization was as follows: 

Division 1 — Ballistic Research 

Division 2 — Effects of Impact and Explosion 

Division 3 — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Explosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 11 — Chemical Engineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 

Division 15 — Radio Coordination 

Division 16 — Optics and Camouflage 

Division 17 — Physics 

Division 18 — ^War Metallurgy 

Division 19 — Miscellaneous 

Aj)plied Mathematics Panel 

Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration Administrative Committee 


IV 


53 


NDRC FOREWORD 


A s EVENTS of the years preceding 1940 revealed more 
. and more clearly the seriousness of the world 
situation, many scientists in this country came to 
realize the need of organizing scientific research for 
service in a national emergency. Eecommendations 
which they made to the White House were given care- 
ful and sympathetic attention, and as a result the 
National Defense Eesearch Committee [NDEC] was 
formed by Executive Order of the President in the 
summer of 1940. The members of NDEC, appointed 
by the President, were instructed to supplement the 
work of the Army and the Navy in the development 
of the instrumentalities of war. A year later, upon the 
establishment of the Office of Scientific Eesearch and 
Development [OSED], NDEC became one of its units. 

The Summary Technical Eeport of NDEC is a 
conscientious effort on the part of NDEC to summa- 
rize and evaluate its work and to present it in a useful 
and permanent form. It comprises some seventy vol- 
umes broken into groups corresponding to the NDEC 
Divisions, Panels, and Committees. 

The Summary Technical Eeport of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The first volume of each group’s report 
contains a summary of the report, stating the problems 
presented and the philosophy of attacking them, and 
summarizing the results of the research, development, 
and training activities undertaken. Some volumes may 
be ^^state of the art” treatises covering subjects to 
which various research groups have contributed in- 
formation. Others may contain descriptions of devices 
developed in the laboratories. A master index of all 
these divisional, panel, and committee reports which 
together constitute the Summary Technical Eeport 
of NDEC is contained in a separate volume, which 
also includes the index of a microfilm record of per- 
tinent technical laboratory reports and reference 
material. 

Some of the NDEC-sponsored researches which had 
been declassified by the end of 1945 were of sufficient 
popular interest that it was found desirable to report 
them in the form of monographs, such as the series 
on radar by Division 14 and the monograph on sam- 
pling inspection by the Applied Mathematics Panel. 
Since the material treated in them is not duplicated 


in the Summary Technical Eeport of NDEC, the 
monographs are an important part of the story of 
these aspects of NDEC research. 

In contrast to the information on radar, which is 
of widespread interest and much of which is released 
to the public, the research on subsurface warfare is 
largely classified and is of general interest to a more 
restricted group. As a consequence, the report of 
Division 6 is found almost entirely in its Summary 
Technical Eeport, which runs to over twenty volumes. 
The extent of the work of a division cannot therefore 
be judged solely by the number of volumes devoted 
to it in the Summary Technical Eeport of NDEC : 
account must be taken of the monographs and avail- 
able reports published elsewhere. 

Though the Committee on Propagation had a com- 
paratively short existence, being organized rather late 
in the war program, its accomplishments were defi- 
nitely effective. That so many individuals and organ- 
izations worked together so harmoniously and con- 
tributed so willingly to the Committee’s efforts is a 
tribute to the leadership of the Chairman, Charles E. 
Burrows. The latest information in this field was 
gathered from the four corners of the earth, organized, 
and dispatched to the points where it would aid most 
in the prosecution of the war. 

Much credit must be given, not only to the members 
of the Committee and its contractors, but also to the 
many other individuals who gave so generously of 
their time and effort. This group included a number 
of our Canadian and British allies. In addition to the 
assistance given the war effort, a considerable contrib- 
ution has been made to the knowledge of short-wave 
transmission and especially to the interrelation of this 
phenomenon with meteorological conditions. Such in- 
formation will be most valuable in weather forecasting 
and in furthering the usefulness of the whole radio 
field. 

Vannevar Bush, Director 
Office of Scientific Research and Development 

J. B. CoNANT, Chairman 
National Defense Research Committee 


V 




FOREWORD 


T he success of the propagation program was the 
result of the wholehearted cooperation of many in- 
dividuals in the various organizations concerned, not 
only in this country but in England, Canada, New 
Zealand, and Australia. The magnitude of the research 
work accomplished was possible only because of the 
willingness of the workers in many organizations to 
undertake their parts of the overall program. In fact, 
the entire program of the Committee on Propagation 
was carried out without the necessity of the Committee 
exercising directive authority over any project. 

Dr. Hubert Hopkins of the National Physical Labo- 
ratory in England and Mr. Donald E. Kerr of the 
Radiation Laboratory at the Massachusetts Institute 
of Technology, who were working on this phase of the 
war effort when the Propagation Committee was 
formed, were instrumental in giving a good start to 
its activities. The largest single group working for the 
Committee was under Mr. Kerr. 

The existence of a common program for the United 
Nations in radio-wave propagation resulted from the 
splendid cooperation given the Propagation Mission 
to England by Sir Edward Appleton and his Ultra 
Short Wave Panel. Later, through the cooperation of 
Canadian engineers and scientists. Dr. W. R. Mc- 
Kinley of the National Research Council of Canada 
and Dr. Andrew Thomson of the Air Services Meteor- 
ological Division, Department of Transport, Toronto, 
Canada, undertook to carry on a part of the program 
originally assigned to the United States. The program 
was further rounded out by the willingness of the New 
Zealand Government to undertake an experiment for 
which their situation was particularly favorable. Dr. 
F. E. S. Alexander of New Zealand and Dr. Paul A. 
Anderson of the State College of Washington initiated 
this work. Needless to say, the labor of the Committee 
on Propagation could hardly have been effective with- 
out the cooperation of the Army and Navy. Maj. Gen. 
H. M. McClelland personally established Army co- 


operation, and Lt. Comdr. Ralph A. Krause and Capt. 
Lloyd Berkner were similarly helpful in organizing 
Navy liaison and help. 

Officers and scientific workers of the U. S. Navy 
Radio and Sound Laboratory at San Diego, California, 
altered their program on propagation to fit in with the 
overall program of the Committee. Capt. David R. 
Hull, Bureau of Ships, understanding the importance 
of the technical problems, paved the way for effective 
cooperation by this laboratory. 

Dr. Ralph Bown, Radio and Television Research 
Director, Bell Telephone Laboratories, integrated the 
research programs undertaken by Bell Telephone 
Laboratories for the Committee on Propagation. This 
joint research program included meteorological meas- 
urements on Bell Telephone Laboratories property by 
meteorologists of the Army Air Forces working with 
Col. D. N. Yates, Director, and Lt. Col. Harry Wexler 
of the Weather Wing, Army Air Forces. The accom- 
plishments of the Committee on Propagation are a 
good example of the effectiveness of cooperation — all 
parts were essential and none more than the rest. 

I want to thank Dr. Karl T. Compton, President of 
Massachusetts Institute of Technology, who was al- 
ways willing to discuss problems of the Committee and 
who helped me to solve many of the more difficult 
ones, and also. Prof. S. S. Attwood, University of 
Michigan, whose continual counsel throughout my 
term of office was in no small way responsible for the 
success of our activity. 

Credit is also due Bell Telephone Laboratories, 
which made my services available to the Government 
and paid my salary from August 1943 to September 
1945, and to Cornell University, which has allowed 
me time off with pay to complete the work of the 
Committee on Propagation since September 1945. 

Chas. R. Burrows 

Chairman, Committee on Propagation 


vii 






PRE FACE 


O NE OF THE important contributions of the NDEC 
Committee on Propagation of permanent value is 
the publication of the technical papers presented at 
the several Conferences on Propagation, and the pub- 
lication of documents prepared for the Committee 
under contract OEMsr-1207 by the Columbia Univer- 
sity Wave Propagation Group. 

The first Conference was held at the Eadiation 
Laboratory at Massachusetts Institute of Technology 
in July 1943 prior to the formation of the Committee 
on Propagation. Those sponsored by the Committee 
were the 2nd, 3rd and 4th Conferences held, respec- 
tively, in New York, February 1944; in Washington, 
November 1944; and in Washington, May 1945. 

The bulk of the material published is taken from 
the Columbia University reports and from the papers 
presented at the 3rd and 4th Conferences; the re- 
mainder comes from the 2nd conference. By careful 
selection it has been possible to avoid excessive repeti- 
tion; and yet on continuing projects, such as trans- 
mission studies, it is possible to follow their develop- 
ment over a considerable period of time. 

Some of the material has been published in Volume 
1 of this series — that dealing with the theoretical as- 
pects of propagation, both standard and nonstandard. 
In this volume the reader first finds, in Part I, a sum- 
marizing review of six transmission experiments car- 
ried out in widely separted geographical locations : 
namely, Massachusetts Bay, San Diego, Arizona, An- 
tigua, West Indies, and Great Britain. The basic 
objectives here have been to learn the facts concerning 
transmission and, as far as possible, to correlate them 
with the transmission theory given in Volume 1 and 
with the meteorological factors presented in this 
volume. 

In Part II of this volume the subject considered is 
meteorology : first theory, then equipment, and finally 


the development of forecasting techniques in which the 
ultimate goal is the ability to predict radio perform- 
ance from meteorological measurements made consid- 
erably earlier. 

In Part III, Chapter 9, on reflection coefficients, 
presents a certain amount of new material which, how- 
ever, tends to confirm previous views and further sub- 
stantiates formulas already available. 

In Chapter 10, on dielectric constant, absorption, 
and scattering, the reader will find a considerable 
volume of new material. With increasing frequency 
the absorption by the components of the atmosphere 
becomes increasingly important while the problems of 
absorption and scattering, as related to frequency and 
water droplet size, bear importantly on the ability to 
track clouds and storms by radar. This problem, storm 
detection (Chapter II), was interestingly presented 
by Canadian scientists in the form of a movie of the 
PPI of a radar tracking snow and thunder storms. 
The written report must necessarily be less complete. 

In Chapter 12, on echoes and targets, the reader 
will find an interesting treatment of some of the more 
unusual problems concerning the radar behavior of 
targets. Volume 2 closes with a consideration of an 
angle-of-arrival experiment. 

Space limitations have made it impossible to include 
a few reports, but these, together with numerous sup- 
porting documents listed in the Columbia University 
Wave Propagation Group bibliography, have been 
microfilmed. 

Acknowledgment is due to the many authors who 
have contributed to this series, not only for the mate- 
rial and its oral presentation at the Conferences, but 
also for their willingness to prepare the material in 
form for permanent record. 

Stephen S. Attwood 
Editor 


IX 






CONTENTS 


CHAPTER 1 PAGE 

PART I 

TRANSMISSION EXPERIMENTS 

1 Transmission Experiments over Massachusetts Bay . 3 

2 Transmission Experiments near San Diego .... 19 

3 Transmission Experiments in Arizona 29 

4 Transmission Experiments at Antigua, West Indies . 33 

5 Transmission Experiments in England 47 

PART II 

METEOROLOGY 

6 Meteorology — Theory 63 

7 Meteorology Equipment for Short Wave .... 97 

8 Meteorology — Forecasting 107 

PART III 

MISCELLANEOUS EXPERIMENTS 

9 Reflection Coefficients 137 

10 Dielectric Constant, Absorption and Scattering . . . 148 

11 Storm Detection 187 

12 Echoes and Targets 191 

13 Angle-of- Arrival Measurements 205 

Bibliography 213 

OSRD Appointees 219 

Contract Numbers 221 

Service Project Numbers 222 

Index 223 






PART I 

TRANSMISSION EXPERIMENTS 




Chapter 1 

TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


MICROWAVE TRANSMISSION IN 1944 — 
GENERAL DESCRIPTION'^ 

T his paper describes the general features of the 
work on atmospheric refraction undertaken during 
the summer and fall of 1944 ; other papers by members 
of this group will describe specific phases. The results 
described must be considered strictly tentative. They 
are the outcome of a hasty survey of a large amount 
of experimental data which ceased to accumulate 
only a short time before this report was prepared. 
Consequently, it has not been possible to do more 
than abstract the most obvious information. 

The principal objectives of the present program 
were : 

1. To study the modification of continental air by 
the ocean surface and from this study to improve the 
technique of forecasting modified index curves at low 
altitudes over water. The reason for the detailed 
meteorological study is that when beginning this work 
we believed that the existing ideas of the physical 
phenomena involved in producing low-level modifi- 
cation were not on a sufficiently sound basis to allow 
a direct analytical approach. 

2. To study experimentally one-way and radar trans- 
mission through the range of refraction conditions 
varying from substandard to trapping. Particular em- 
phasis was to be placed on wavelength dependence, 
and, when possible, information was to be obtained on 
vertical coverage patterns under these various refrac- 
tion conditions. 

Radio Program 

The radio part of the project employed a combina- 
tion of one-way and radar apparatus operating over 
Massachusetts Bay. Two paths were chosen for one- 
way transmission; one was the 22-mile path^ from 
Deer Island (Boston Harbor) to Eastern Point 
(Gloucester) and the second a 41-mile path farther 
from the shore line (Eastern Point, Gloucester, to 
Race Point, Cape Cod; see Figure 1). Over the 22- 
mile path, transmission was on S band, while on the 
41-mile path one-way transmission was on 117 me and 

•By D. E Kerr, Radiation Laboratory, MIT. 


on S, X, and K bands. Radar sets on S and X bands 
were placed at the transmitter site for the latter path. 

On the short path the terminals were placed so as 
to give approximately grazing incidence, but on the 
long path the terminals were well below the horizon. 



At the transmitting terminal of the one-way circuit 
were two radar sets on X and S bands; from this 
location they could scan the Xew England coast line 
to measure signal strength from fixed targets. 

Note that the short path is close to the coast line, 
while the longer path is considerably farther away 
and is so located that approximately westerly winds 
undergo appreciable modification by the time they 
have reached the transmission path. 

Transmitters 

The transmitter for the short path was located at 
Deer Island about 120 ft above mean sea level and 


3 


4 


TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


supi)lied approximately 1 w to a paraboloidal antenna 
30 in. in diameter. 

The transmitter site for the other transmission path 
and the trucks housing the two radar sets were at 
Race Point (Provincetown). The radar sets operate 
on the S and X bands and are approximately 50 ft 
above mean sea level. They both have antenna diam- 
eters of 4 ft and a ratio of transmitted power to 
minimum detectable power of approximately 167 db. 
These sets were operated from August 1st through 
October 20th. The measurements consisted of 
hourly determination of the strength of echo from 
four specially selected targets and of recording maxi- 
mum detection range on fixed targets over water look- 
ing up the coast line ; in addition, plan position in- 
dicator [PPI] photographs were taken at hourly 
intervals. The performance of the radar sets was care- 
fully monitored by appropriate means for determina- 
tion of transmitted power and minimum detectable 
received power. All echo signal strengths were meas- 
ured in absolute values with a signal generator 
coupled to the S 3 'steni. The records of signal strength 
from the four selected targets and those of maximum 
detection range were plotted and returned to the 
laboratory on a weekly basis. 

The tower carrying the one-way transmitting equip- 
ment consisted of the bottom half of a 100-ft SCR-271 
tower. The house at the foot of the tower served as 
operations headquarters, while the top house con- 
tained the transmitters. The 117-mc antenna was a 
five-element Yagi array projecting horizontally from 
the forw'ard corner of the top of the house. The X- 
and S-band antennas were paraboloids 4 ft in diam- 
eter, made of close-spaced grid work designed to 
reduce wind resistance. The feed for each of these 
antennas was a dummy-dipole array excited from the 
open end of a wave guide projecting through the 
vertex of the paraboloid. The K-band antenna was a 
paraboloid 2 ft in diameter, illuminated by a small 
horn. Polarization was horizontal for practically the 
entire period of the program. 

All the microwave antennas were provided with a 
scheme for rendering them independent of rain. A 
blast of air from inside the house was injected into 
the wave guide at the transmitter by means of a 
blower. This stream of air effectively prevented ac- 
cumulation of a film of water on the inside of the 
guide feed. 

The transmitter used on 117 me was one from an 
SCR-624 A^HF (very high frequency) communica- 
tion set. Its frequency was quartz-crystal controlled, 


and it delivered approximately 10 w of c-w j^ower 
into a balanced line connected to the Yagi antenna. 
The output power of the transmitter was monitored 
continuously on an Esterline-Angus recording mil- 
liammeter. 

The S- and X-band transmitters employed pulsed 
magnetrons operating at a pulse recurrence frequency 
of 700 c with a pulse length of 1.5 /x sec and a peak 
power output of approximately 10 kw. The output 
pulse from the modulator was continually checked by 
the synchroscopes, and a check was made of the trans- 
mitted radio frequency spectrum of the pulses by 
means of the spectrum analyzer. 

Both S- and X-band transmitters were provided 
with continuously recording monitors operating Ester- 
line-Angus recording milliammeters. Several types 
of monitor circuits were emj^loyed during the course 
of the program, but the one which proved most satis- 
factory employed a thermistor bridge coupled by 
means of wave selector, or directional coupler, to the 
wave guide between transmitter and antenna. Daily 
calibrations of the recording thermistor bridge cir- 
cuits were made, providing a constant check of power 
output in absolute values. In addition to recording 
of average power output by frequent checking of 
spectrum and high-voltage iDulse, the cathode current 
of the magnetrons was also recorded. 

The K-band transmitting equipment differed from 
the S- and X-band equipment only in matters of 
unessential detail. 

Receivers 

The receiving terminal of the one-way transmission 
circuit is located at Eastern Point, Gloucester; the 
receivers were mounted in a 100-ft tower similar to 
the one at Provincetown. There were two sets of re- 
ceivers, one approximately 136 ft above mean sea 
level in a house at the top of the tower and the other 
approximately 30 ft above in a house at the bottom 
of the tower. The receiving antennas are identical 
with those for the transmitters. 

The K-band receiver was a superheterodyne spe- 
cially constructed for this purpose and put into opera- 
tion late in the experiment. It had a bandwidth of 
14 me but no automatic frequency control [AFC], 
with the consequence that it required constant attend- 
ance to produce a satisfactory record. The receiver 
for the Deer Island circuit was a narrow-band c-w 
receiver of the type used in last year’s experiments 
and described in reference 1. 


MICROWAVE TRANSMISSION IN 1944^GENERAL DESCRIPTION 


5 


The X- and S-baiid receivers deserve mention be- 
cause of their special characteristics, wliich were de- 
veloped to meet the requirements of this work. They 
are provided with AFC circuits arranged to search 
for a lost signal automatically. Having found the 
signal, the circuit locks the receiver in tune and con- 
tinues recording. These receivers have specially de- 
signed automatic gain control circuits providing es- 
sentially logarithmic response of 70- to 80-db range 
well spread across the recorder scale. The minimum 
detectable power for these receivers is approximately 
110 db below 1 w for both S band and X band, and 
the minimum signal required for satisfactory opera- 
tion of the AFC is approximately 105 db below 1 w. 
The latter figures are important for this particular 
setup, since they determine the usefulness of the re- 
ceivers in studying signal strength near or below that 
encountered under standard refraction conditions. 

The receivers were calibrated daily by means of 
signal generators coupled permanently to the wave 
guide between the antenna and the receiver through 
wave selectors with known fixed coupling losses. Very 
close check on performance was maintained so that 
the receivers at all times gave an accurate indication 
of the absolute value of received signal strength. 

The arrangement of S- and K-band receivers in 
the house on top of the tower was similar to that in 
the lower house, but the K-band receiver was of a less 
sensitive type requiring no tuning. There was a 117- 
mc receiver in the top house but not in the bottom 
house, and there was no receiver for the Deer Island 
circuit in the top house. 

The outputs of all eight receivers were wired direct- 
ly into an Esterline-Angus recording milliammeter. 
With this arrangement one operator was able to keep 
continuous watch on the performance of all receivers 
and was required to climb the tower only when major 
adjustments of the top receivers were necessary. 

The Gloucester station was the control station for 
the radio network formed by all the stations involved 
in the project. The transmitter station at Province- 
town, each of the radar trucks, the fixed meteoro- 
logical stations, the boat, and one of the airplanes 
were all equipped to operate radiotelephone on 3.5 me, 
thus allowing rapid and efficient exchange of informa- 
tion essential to the operation of all units involved in 
the program. 

Meteorological Program 

The meteorological phase of our program con- 


sisted of two main parts: (1) meteorological meas- 
urements, and (2) forecasting and analysis. 

All meteorological measurements were made with 
varying versions of the psychrograph, earlier models 
of which are completely described in reference 2. 
This instrument measures wet and dry bulb tempera- 
tures as a function of height, using the electrical re- 
sistance thermometer principle. From these measure- 
ments the M curve is constructed. 

The meteorological soundings were made in the 
Massachusetts Bay area with psychrographs carried 
by two aircraft, by captive balloons operating from a 
boat and from two fixed land stations. The boat 
operated in the Bay and out to about 100 miles off- 
shore, while the aircraft operated as far as 170 miles 
offshore. It should be mentioned that aircraft sound- 
ings of this type are rather hazardous, since they in- 
volve descending to altitudes of approximately 20 ft 
at large distances from land. 

The fixed meteorological stations were located at 
Duxbury and Race Point. The Duxbury location was 
chosen to place the sounding station near enough to 
the shore to obtain a representative sample of the air 
just leaving the land. 

The Race Point meteorological station was located 
at a position to allow soundings at the water’s edge 
on the westernmost extremity of the top of Cape Cod. 
The primary purpose of this station was to measure 
the characteristics of the air after it had been sub- 
jected to the influence of the ocean surface between 
the mainland and the station. This location allowed 
measurements over a range of wind directions of ap- 
proximately 180°, but no relevant soundings could be 
made when the wind had an easterly component, since 
the air would have had a land trajectory for at least 
a short period. It was necessary to take all soundings 
very close to the water’s edge to prevent solar heating 
of the beach from influencing the bottom of the meas- 
ured M curve. At both Duxbury and Provincetown 
soundings were taken on a prearranged schedule 
which, when possible, involved both day and night 
operation. Soundings, surface wind velocities and 
hourly observations of sky conditions, etc., were made 
at both Duxbury and Race Point. The water tempera- 
ture was also measured at the Provincetown station. 

A 60-ft pole was erected at Race Point carrying 
four anemometers, four psychrographs, and a wind 
direction indicator. The original scheme involved con- 
tinuous recording of temperature, humidity, and wind 
speed at four levels by means of the instruments on 
the pole, but unfortunately a large sand bar formed 


6 


TKANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 




Figure 2. Microwave signal types, 




RADIO AND RADAR TRANSMISSION MEASUREMENTS 


7 


ill front of the pole soon after it was erected and 
caused sufficient disturbance of the air in the lowest 
levels that such measurements were not feasible. The 
psychrograph, anemometer, and wind direction in- 
dicator at the top of the pole continued to be useful, 
however, and provided the continuous information 
recorded by the station. 

A 50-ft boat, the Wanderer, was used for making 
measurements in Alassachusetts Bay. The psychro- 
graph used for measurements from 2- to 48-ft eleva- 
tion is attached to a cable running between a boom 
extending outward from the side of the ship and an 
extension to the top of the mast. A similar psychro- 
graph was used for soundings to higher levels, operat- 
ing from the winch at the rear of the boat. Further 
essential meteorological information was provided by 
the boat in frequent measurements of surface water 
temperatures in Massachusetts Bay. A direction-find- 
ing loop was used to determine position at great dis- 
tances off shore. 

12 RADIO AND RADAR TRANSMISSION 
MEASUREMENTS^ 

The purpose of this paper is to describe the results 
of a rough preliminary analysis of the transmission 
experiment. A thorough analysis must await the com- 
pletion of the meteorological study, since the trans- 
mission depends directly upon the meteorological 
conditions over the path of the radiation. The em- 
phasis here will therefore be mainly on the strictly 
radio data with only qualitative reference to the 
meteorological information. 

One-Way Transmission 

The values of the transmitted powers, antenna 
gains, and receiver characteristics were chosen so as 
to make the standard signal level, as computed for the 
receivers at the top of the tower, well above the mini- 
mum detectable level and the minimum level at 
which the automatic frequency control [AFC] and 
AFC search are effective. Sufficient compression was 
used to give a range of about 60 db for useful recep- 
tion, which had been expected to be enough for the 
variations due to atmospheric conditions. It turned 
out, however, that additional range was needed, es- 
pecially in the direction of greater signal strengths; 
to accommodate additional received power, attenua- 


tors were inserted in the lines. Thus the actual range 
of values observed is at least 90 db at the microwave 
frequencies and 40 db at 117 me. 

Signal Types 

Figure 2 shows that the types of signal observed 
at the microwave frequencies (S and X) are not 
essentially different from those observed in previous 
tests on a shorter path. The first type is high signal 
on the average, well above the standard level, with 
roller fades which may go down to the minimum de- 
tectable level and with periods of 2 minutes to an 
hour or so. These periods are generally shorter at 
any time on X than on S band. When this type of 
signal is present on S band it is almost invariably 
present on X band also and on both paths. It always 
occurs simultaneously on the high and low receivers 
at any frequency. 

The second type is high and steady. Its level may 
be anywhere from 5 to about 30 db above the stand- 
ard, generally higher on X band than on S band. 
Most of the time this type of signal occurred simul- 
taneously on S and X, but there were some occasions 
when the S-band signal was of the high and steady 
type Avhile the X-band signal became of the first 
type, high with roller fades. 

The third kind of signal is about standard and 
fairly steady. (This may be a limiting case of tlie 
high and steady variety.) It does not necessarily 
occur on both frequencies and on both high and low 
receivers at the same time. 

The fourth type is standard on the average, with 
scintillation of more than 10 db. The preliminary 
analysis has not revealed the reasons, or any correla- 
tions, for the difference between this and the preced- 
ing type ; it is certainly nothing obvious, such as wind 
speed, for example; and it may occur on either fre- 
quency when the other is steady. 

The fifth type is the blackout,” below standard 
and variable. This signal type is strongly scintillat- 
ing. It occurs simultaneously on both frequencies, 
both paths, and on high and low receivers (except 
possibly for low X, where the difficulty mentioned 
above of determining an average value of something 
very low on the scale is important). 

Figure 3 shows the signal types observed at 256 
cm. These are distinct from those observed at the 
microwave frequencies not only in appearance but 
also in times of occurrence. In general no relation has 
been found to exist between the types at the two 


'’By Pearl Rubenstein, Radiation Laboratory, MIT. 


oe 8ELO» I W4BT OB BELOW t WATT OB BELOW I WATT 06 BELOW I WATT OB BELOW I WATT 


8 


TRANSMISSION EXPERIMEN PS OVER MASSACHUSETTS RAY 



FiciUHE 3. Signal types at 250 cm (117 me) 


RADIO AND RADAR TRANSMISSION MEASUREMENTS 


9 


frequencies altliougli on rare occasions such a relation 
is indicated ; indeed the type may remain constant on 
one and change on either of the others. Steady signal 
is most frequent at 256 cm, but the other types shown 
also occur fairly often. Variations of 30 to 40 db 
overall take place, and the variations may be fast or 
slow. 

Statistics 

A fairly detailed statistical study has been made of 
the S and X signals at the top level. These were 
chosen because they were available for the longest 
periods, and because they gave the most reliable re- 
sults (because of the receiver characteristics the re- 
lation of the standard to the minimum detectable 
level was most suitable). The other microwave records 
gave similar results. As for the 256-cm transmission, 
the most important result was that the signal level 
was above the minimum detectable very nearly 100 
per cent of the time, although fades to this level were 
fairly frequent. If a choice had to be made of the 
most reliable frequency for transmission over the 
circuit, there would be no question in the choice of the 
longer wavelength. 

The statistics available on K band are very similar 
to those on X band as far as can be determined. 
Signal levels less than about 20 db above standard 
cannot be detected on the K band. 

The study was made of the average signal level on 
a weekly basis; it showed marked differences from 
week to week, depending upon the specific weather 
situation. For purposes of the statistics a range of 
values around the standard was included in the 
standard signal (allowance for scintillation, tides, 
etc.). This range was taken as ±5 db on S band and 
±10 db on X band, values determined by inspection 
of the entire record and thought to give comparable 
results. 

The most interesting result of this analysis was 
the discovery that standard signal occurs extremely 
rarely over this path. High signal is most frequent; 
depending upon the wavelength and the season of the 
year, substandard and standard signal occur less fre- 
quently. In the summer no significant frequency de- 
pendence was observed in the statistics. Some typical 
weeks gave the figures shown in Table 1. 

As the season progressed to the fall, however, sev- 
eral related trends became apparent: (a) the increas- 
ing incidence of standard signal, especially on S 
band; (b) the increasing incidence of high, steady 


Table 1. Statistics of S- and X-band transmission in 
summer. 


Date 

Per cent of 
time above 
standard 

Per cent of 
time below 
standard 

Per cent 
of time 
standard 

July 10-16 

63 

36 

1 

Aug. 21-27 

97 

3 

0 

Aug. 28-Sept. 3 

80 

15 

5 


signal, especially on X band, with the level higher 
above the standard on X than on S; (c) the fre- 
quency effect on the incidence of above-standard 
signal indicated in (b) ; and (d) the decreasing oc- 
currence of substandard signal. These trends are illus- 
trated in Table 2. 


Table 2. Statistics of S- and X-band transmission in 
the fall. 


Date 

Per cent of 
time above 
standard 

Per cent of 
time below 
standard 

Per cent 
of time 
standard* 

Sept. 25-Oct. 1 

S 

58 

15 

27 


X 

80 

10 

10 

Oct. 16-22 

s 

76 

2 

22 


X 

92 

0 

8 


*By this term is to be understood the percentage time in which the 
signal is ± 2.5 db of standard on S band and ± 5 db on X band. 


Xo diurnal effect was found in the signal except 
under some very special circumstances. Not only was 
no such trend apparent upon visual inspection, but 
also an analysis of the material by 6-hour intervals 
confirmed appearances. 

Correlations 

In addition to the statistical study, another type 
of analysis has been made to look for correlations 
between the variations of signal strength with fre- 
quency at a given location or with height at a given 
frequency. Figures 4 to 6 show some typical graphs 
of such correlations, each point representing average 
hourly values, for 1 week. Figure 4 shows the varia- 
tion of the high S- and X-band signal strengths. It 
is clear that in most cases the two wavelengths change 
together. This was the predominant behavior through- 
out the summer. The notable exceptions are those 
points where X is high and S nearly standard; this 
is the frequency effect remarked in the discussion 
of the high and steady signal which became common 
in the fall. As will be seen later, this occurs with 
very low modified index inversions, less than 20 ft 
high. 


10 


TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


Figure 5 shows the relation between S-band signal 
strengths for high and low receivers; the correlation 
is excellent in practically every case. A similar cor- 
relation exists for the high and low X-band signal, 


'high 

RECEIVE! 

RS 


SEj 

>T Ij 

CM X 

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1- 

100 80 60 40 20 

DB BELOW 1 WATT 
S BAND 


Figure 4. Relation between S- and X-band signal 
strengths. 


except for the case of very low signal where the ap- 
parent average value of the signal strength on the 
low receiver is always relatively high. Whether this 


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SI 

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100 80 60 40 

DB BELOW 1 WATT 
HIGH RECEIVER 


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20 


Figure 5. Relation between signal strengths at high 
and low receivers. 


is caused by the lack of receiver sensitivity or is a 
real transmission phenomenon cannot be conclusively 
decided on the basis of the present information. 

Figure 6 shows the relation of signal strengths at 
117 me and S band; the difference between this figure 
and the preceding two speaks for itself. From the pre- 
liminary analysis no consistent correlation has been 


found between the behavior of the low- and high- 
frequency transmission. 


HIGH ' 
RECEIVERS 


s' 

EPT i 

8-24 

^ 194 

4 


























X 

X 


JS 





if'. 

/j 


A 


L 




i % 


X * 

X 

9 

X ’ 







100 80 60 40 20 

DB BELOW 1 WATT 
S BAND 


Figure 6. Relation between 117-mc and S-band signal 
strengths. 


The variations on the two paths are generally in 
good agreement although changes in signal type rare- 
ly occurred exactly simultaneously; the changes on 
the short path are always less in magnitude than on 
the other, as would be expected. 

As far as can be determined from the available 
data the K-band signal correlates quite well in gen- 
eral with that on S and X bands. Only high signal 
can be observed, of course, with the present equip- 
ment. 


Relation of Radio Results to Modified 
Index Curves 

Detailed conclusions must await the full analysis 
of the data. At present certain qualitative conclu- 
sions can be drawn: 

1. When the surface modified index inversions are 
present, the microwave signal level is high on the 
average, and usually the signal has roller-type fades. 

2. When the M curve is substandard the signal is 
low and scintillating. The M curves which are stand- 
ard all the way down to the surface of the water 
appear to be very rare, even when the air is colder 
than the water. The previous results on the short 
path had tended to discount the importance of the 
low M inversions which exist over water most of the 
time, especially with cold air flowing out from the 
land. The increased sensitivity of the present setup 
to variations in the M curve, the additional path 
length, and finally the inclusion of the X-band trans- 
mission on the circuit have shown definitely that such 
low M inversions are far from negligible but will 
affect S-band communications (or one-way trans- 


RADIO AND RADAR TRANSMISSION MEASUREMENTS 


11 


mission) and both one-way and radar transmission on 
X band. The signal occurring with these M inver- 
sions less than 20 ft high is usually the high, steady 
type. It is generally not quite so high in average level 
as that characterized by roller fades found with larger 
M inversions. 

3. The high, steady signal occurring with very 
low M inversions reveals the only clear-cut cases of 
frequency diversity between S and X bands. In this 
case a variety of combinations has been found : nearly 
standard signal on S band with X-band signal from 
10 to 30 db above standard; S band 10 to 15 db above 
standard with X band 30 or so db above standard; 
and finally S band about 20 or more db above stand- 
ard and steady while X band changes to the first sig- 
nal type : high with fades. 

4. One of the most interesting features of the trans- 
mission is the fact that at any given location, for a 
fixed frequency, the increase in field strength is lim- 
ited; that is, no matter how much the M inversion 
increases in height or in strength beyond a certain 
value (which is as yet unspecified) the average value 
of the signal strength does not continue to increase 
but rather remains the same within about 10 db. This 
^^saturation” level is of the order of the free space 
value. (Maximum level goes up to 12 to 15 db above 
free space but only infrequently.) Consequently, the 
level reached on a given path appears to be indepen- 
dent of the receiver height (within the height range 
covered in these measurements), the height-gain effect 
which exists under standard conditions being essen- 
tially eliminated when shore trapping takes place. 
Under some conditions, especially when the signal is 
high with fading but has not yet reached the satura- 
tion level, the lower of the two receivers has been ob- 
served to receive higher signal than the higher one. 
With stronger signal the values on the two become 
nearly identical, as has been stated. 

These results agree with unpublished calculations 
made for several values of duct height and M deficit 
for S band, of the first transmission mode alone, 
which indicate that the height-gain effect should dis- 
appear and the signal approach a certain saturation 
level. Thereafter, calculations show, the contribution 
of the first mode decreases, but the observations sug- 
gest that perhaps the other modes continue to cause 
the average level to reach approximately the same 
value, as duct height and M deficit continue to in- 
crease. 

It has been found that, with an M inversion over 
only a portion of the path and a standard curve on at 


least a small part of it, the signal type may be high 
with roller fades and the average level high, so that 
the record is indistinguishable from that which oc- 
curs with more uniform conditions. 

Radar Transmission 

From Race Point, targets were available over water 
at ranges of 20 to several hundred miles along the 
coast of Massachusetts and Maine, plus some addi- 
tional targets inland and whatever shipping was in 
the vicinity. Of the coastal targets four were chosen 
for regular observation. These were fairly isolated 
fixed targets, the echoes from which appeared to be 
relatively steady in several days’ observations, at 
ranges of 22, 41, 65, and 73 statute miles. Absolute 
power measurements of the returns of each of these 
targets (whenever visible) were made hourly by com- 
parison with a signal generator. Each measurement 
represents the maximum value of the signal during 
a period of 1 to 3 minutes. This differs rather essen- 
tially from the hourly averages of the one-way data. 

In addition to signal strength measurements, hour- 
ly observations were also made of the maximum ranges 
obtained on surface targets, and plan position indi- 
cator [PPI] photographs were made which reveal 
at a glance many interesting features of the radar 
coverage which are hard to describe briefly in words. 
The maximum sweep length available on the PPI 
was 140 miles for the S-band set and 115 miles at X 
band. Additional range was available on the delayed 
A-scope sweeps, so that the maximum was 180 miles 
for most of the period of observations. This was ex- 
tended to 280 miles for the last week of the test. 

In addition a portable K-band radar set was set up 
near Race Point Light only 17 ft above mean sea 
level and regular observations of range were made and 
shipping tracked. 

Target Signal Strengths 

The strength of the echoes from the four targets, 
including the nearest one which is ordinarily visible 
both optically and by radar, varied from below mini- 
mum detectable to at least 60 db above for the two 
nearer targets and about 35 db above for the two 
more distant targets, at both frequencies. In general 
the values of the signal strength were higher for the 
nearer targets, but there were some interesting cases 
when the more distant targets were visible while the 
nearer ones were either not seen or were very weak. 
This may occur at times when the M curve varies 


12 


TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


markedly with direction, as happens occasionally when 
the air trajectory is S or SW or at times of skip dis- 
tance. 

Maximum Ranges 

Large variations in the maximum ranges have also 
been observed at both frequencies, with the upper 
limit apparently being set only by the length of the 
sweep : 280 miles on S band and 200 miles on X band. 
(Note that these radar sets were far from the high- 
power class.) Lack of fixed targets at ranges between 
10 and 25 miles made it impossible to follow in detail 
the way in which substandard conditions reduced de- 
tection range, but there was no question as to the 
general trend toward reduction of range. The maxi- 
mum range of the high sited K-hand receiver [HRK] 
from its location at the Race Point Light was 46 miles 
on a land target and about 30 miles on shipping. 

It should be borne in mind that our project deals 
with propagation near and roughly parallel to the 
coast line. Thus these results are not necessarily ap- 
plicable to operations perpendicular to the coast with 
off-shore winds, where the surface M inversions be- 
come ‘Svashed out.^^ 

Statistics 

The radar observations include about 1,200 hours 
of operation. Of these, overall, the X-band ranges were 
better than ‘"‘normal” 59 per cent of the time (normal 
= 29 miles®) and the S-band ranges 48 per cent of 
the time. At both frequencies ranges were below nor- 
mal 20 per cent of the time. The variations from week 
to week were great, the maximum values being 95 per 
cent above normal on X and 75 per cent above normal 
on S, with about 45 per cent below normal as the 
lowest value at both frequencies. 

Correlations with One-Way Results 

A visual comparison of the radar and one-way data 
suggests fairly good agreement in general between 
the two. To get a more quantitative evaluation of this 
agreement, however, correlation diagrams have been 
drawn. 


“Unfortunately, in the radar case it is impossible to estab- 
lish a precise definition of a “standard” range analogous to 
standard signal in one-way transmission unless detailed in- 
formation is available on the radar target. In this case we 
have attempted to determine the detection range on the low 
hills available as coast line targets, at times when the M 
curve is standard or very nearly so. 


Figure 7 shows such a diagram relating the signal 
strength of the target at Eastern Point as observed 
on the X-band system with the signal strength of the 



SIGNAL STRENGTH 

Figure 7. Relation between one-way and radar trans- 
mission, Race Point to Eastern Point. 

high X-band receiver on the one-way path. As in the 
previous diagrams, a week has been chosen as the time 
interval and hourly values are plotted. In this we 
neglect the difference between the single observation 
of the radar and the average of an houPs continuous 
record in the other case. Note also that all radar 
measurements which give values equal to or below 
the minimum detectable level are plotted at the min- 
imum detectable level; thus if a more sensitive re- 
ceiver had been used, many of these points would have 
fallen lower in the diagram. The diagram reveals the 
nature of the relation: the one-way signal strength 
must rise considerably above the standard value before 
the target becomes visible. Thereafter, small changes 
in the one-way signal correspond to much larger 
changes in the radar echo. As a matter of interest, 
which may or may not be significant, the values at 
times fall close to the square law, as they should if the 
target-refiecting properties remain constant as the 
atmospheric conditions change. 

Figure 8 shows the relation between maximum radar 
ranges on surface targets and the one-way transmis- 
sion results. In this case the effects of both substandard 
and better than standard conditions are noticeable. 
When the one-way signal strength is below standard, 
the radar ranges are mainly less than normal; excep- 
tions occur in cases of strong directional effects and 
S-shaped M curves. As the one-way signal strength 


TRANSMISSION CHARACTERISTICS OF AN OVER-WATER PATH 


13 


rises above the standard level no appreciable increase 
in radar range occurs at first. Only when the one-way 
signal strength has become fairly high do the radar 
ranges begin to increase. Then the entire gamut of 



SIGNAL STRENGTH 

Figure 8. Relation between maximum radar ranges 
and one-way transmission. 

long radar ranges, from about 40 to 280 miles, takes 
place while the one-way signal strength changes only 
slightly. This is another manifestation of the satura- 
tion of the signal at a high value. 

Summary 

Two major conclusions may be drawn from this 
preliminary survey: 

1. Standard signal is the exception rather than the 
rule for microwave radiation on this over- water path 
during the summer and fall. With the high M inver- 
sions which occur with warm, dry air over water, 
signal strengths 30 to 45 db above the standard occur 
about equally often on both, the upper limit being 
approximately the free space value, and radar ranges 


on surface targets are extended to five to ten times 
their normal values. On the other hand, with the low 
M inversions (less than 20 ft, say) which occur with 
air colder than the water, X band is affected more than 
S. Both may experience increases in signal level of 10 
to 30 db above the standard, but the X-band signal 
is high more often than the S and at any given time 
usually reaches a higher level. Radar ranges on sur- 
face targets are extended by as much as 20 to 25 per 
cent above normal, and again X band experiences 
more effect. These increases in signal strength can 
be of great importance for communications, beacons, 
or any other application involving one-way transmis- 
sion of microwaves, such as countermeasure. It should 
also be remembered whenever secrecy is required. 

2. Substandard conditions may be present for sev- 
eral days at a time if the air is warm and moist. The 
reduction in signal strengths and radar ranges on 
surface targets which accompanies substandard con- 
ditions does not seem to be markedly frequency sensi- 
tive. It should be stressed that variations in one-way 
signal strength of at least 90 db have been observed. 
The radar ranges have also varied from roughly 10 or 
15 miles up to at least 280 miles. These changes are 
not rare occurrences; deviations from the standard 
account for the major percentage of the time, especial- 
ly during warm weather, and at the higher frequencies 
even during the fall. 

TRANSMISSION CHARACTERISTICS 
OF AN OVER-WATER FATH^ 

Results were previously reported of some prelim- 
inary analyses of one-way radio transmission on a 41- 
mile over-water path from Provincetown to Gloucester, 


Profile of Tronsmission Poth 
Roco Point To Eottern Point 



Figure 9. Transmission path profiles. (Heights in feet.) 

with terminals well below the horizon. S- and X-band 
radiations were transmitted over the double paths in- 
dicated in Figure 9 to both ‘^high’^ and ^fiow” receivers, 

‘‘By P. J. Rubenstein and W. T. Fishback, Radiation Lab- 
oratory, MIT. 


14 


TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


and 117-mc radiation over only the high path. Numer- 
ous meteorological surface measurements and low-level 
soundings were made, and essentially through compar- 
isons with these measurements the following correla- 
tions for microwave transmission and surface M curves 
were obtained. 

With positive M deficits, or M inversions, two cases 
were found. 

1. Low ducts, less than 50 ft thick, resulted in a very 
steady signal at levels well above standard. The in- 
crease in signal level took place although the terminals 
were as much as 100 ft above the top of the M inver- 
sion. Such low ducts caused greater increases in the 
signal level on X band than on S band. 

2. High ducts, 100 ft thick or more, resulted in very 
high signal levels on the average, but with deep fad- 
ing. The signal level did not continue to increase with 
increasing duct height but instead ^‘^saturated’’ near 
the free space level. No frequency diversity between 
S and X bands was found in this case. 

With negative M deficits, or substandard M curves, 
the signal was always below standard. 

In November 1944 no correlations with M curves 
had been obtained for the 117-mc signal, and a clear 
lack of correlation with the microwaves had been 
noted. 

A detailed analysis has since been undertaken 
which is as yet far from complete. This paper describes 
the method in use and presents some additional results. 

In studying the fundamental phenomena of propa- 
gation the method employed was to tie the complete 
representative M curve to the observed transmission 
results by means of the wave theory. A threefold at- 
tack was used : 

1. The meteorologists studied each situation in de- 
tail to determine a representative M curve and its 
changes with position and time. 

2. Theoretical field strengths were found by put- 
ting the representative M curve, or a close approxi- 
mation to it, back into the wave equation. These theo- 
retical values were then compared with the observa- 
tions. 

3. Empirical correlations were then made between 
tlie M curves and the transmission results. This was 
done because the theory is applicable only to the sim- 
plest M curves and to uniform conditions. 

This approach was employed in an effort to find 
parameters in terms of which predictions of range or 
field strength can be made for operational use. It is 
not considered a suitable method in itself for use in 
the field. 


The meteorological part of the program has not in 
general received sufficient attention. Spot measure- 
ments at a given time and place do not necessarily 
give an adequate description of prevailing conditions. 
A thorough meteorological analysis of the entire period 
of transmission is therefore under way. For each case 
the synoptic situation is studied to find the trajectory 
of the air over the path at the time in question. Radio- 
sondes, surface measurements, winds aloft, measured 
water temperatures, and all available low-level sound- 
ings are studied and the characteristics of the air over 
the water determined. Then representative low-level 
soundings are constructed. Such so-called synthetic 
soundings for the path midpoint are being drawn for 
6-hour intervals for each day of operation. In addition, 
estimates are made of the departures from uniformity 
over the path and of the times of occurrence of marked 
changes. 

All the radio analysis has been based upon these 
synthetic soundings and the accompanying discussion. 
The meteorological analysis is at first made completely 
independent of the radio data, with minor revisions 
when necessary after consideration of the transmis- 
sion data. It is believed that full use of transmission 
data can be made only through such close cooperation 
of the persons engaged in both the meteorological and 
the radio work, not only in the measurements but also 
in the analysis. 

Perhaps tlie most striking information which has 
so far resulted from the detailed analysis is the em- 
pirical correlation of the 117-mc performance with 
M curves. Increases in signal level above the standard 
are found to result from either large surface ducts 
(200 ft or more thick) or elevated superstandard 
layers which do not necessarily show overhanging M 
curves. Such layers occur frequently over Massachu- 
setts Bay, mainly as a result of nocturnal cooling over 
land. Those which affect the 117-mc transmission 
occur below about 1,500 ft. Their strength is usually 
doubtful in view of the lack of accurate information 
on conditions over land in radiation inversions. 

Figure 10 shows the correlation diagrams obtained 
when, first, all points are included, and second, all 
cases of elevated superstandard M layers are omitted. 
(Standard values are — 120 db for 117 me and — 80 
db for S band.) The first diagram obviously shows no 
correlation and is the sort of diagram obtained last 
fall. The second, however, is just what should be ex- 
pected for the correlation with surface phenomena. 
The S-band signal rises to the free space value as the 
duct height goes up to about 100 ft and then ‘^satu- 


TRANSMISSION CHARACTERISTICS OF AN OVER- WATER PATH 


15 


rates” for higher ducts. The 117-inc signal, however, 
is affected only by ducts considerably more than 100 
ft high. Similarly, only a thin substandard layer is 


90 


100 


< 110 


at 


120 


130 


140 

90 


100 


•• • 
• 


•M • • • 


• • 


• m 
• • 


• • *4 
•• • •• 

• • •• • 


• ••• •• 

• • ••<. 

••• • 
• •• *• ••• < • 


• • • 


ALL PERIODS INCLUDED 


'120 


130 


140 







• 

• •• 

• • < 

• 

• • • • 

• 

• • 

• •• 

• 1 
•• 

• 

• 

• 

• • 

. 1 

•• 

• ••• •• • 
• • •• • 
• • ••••• 

• • • < 
• ♦•••• 

_ • • 
«■••••• i 

» • ••• _ • 

: 

• 

• 

• •• • • • 

• • • 

••• • 
•• •• 

• • 

• 

• • • 
• • •• 

• 

• •• 

• 

• 

• 

• • •••••• 

«• 

• 

• •• 


• 

• 

PERIODS 
M LAYE 

1 

OF SUPERS' 
RS ALOFT Oh 

1 1 

FANDARD 

FITTED 


100 


80 60 40 

DB BELOW 1 WATT 
HIGH S BAND 


20 


Figure 10. Field strengths: 117 me and S band, July 
31 to August 17, 1944. 


signal level was above standard 49 per cent of the 
time, standard 38 per cent of the time, and substand- 
ard 13 per cent of the time. Of the superstandard 
period 46 per cent has been correlated with elevated 
superstandard M layers, 36 per cent with thick sur- 
face ducts, and 4 per cent with situations in which 
elevated layers and thick surface ducts coexisted. Only 
14 per cent of the time remains in doubt, and this in- 
cludes many periods of exceedingly complex meteoro- 
logical situations for which the analysis was incon- 
clusive. In addition to correlation of field strengths 
with M curves, comparisons have been made between 
measured and theoretical values of field strengths. The 
theoretical values were calculated on the assumption of 
bilinear modified index curves, that is, curves made 
up of two straight-line segments. The M curve is taken 
to be standard above the joint, tod two parameters are 
used: the height of the joint, or duct thickness, g, and 
the ratio s of the slope. The straight lines are drawn 
not in terms of M deficits but to give the best possible 
fit to the actual M curve. For the range of values of 
these parameters for which the contribution of the first 
mode only is of importance the curves of field strength 
shown in the following two figures are representative. 

Figure 11 shows the effect of changing duct height, 
0 to 500 ft, on the 117-mc field strength for various 
values of the slope of the lower segment. The field 



DUCT HEIGHT IN FEET 


Figure 11. Theoretical field strength versus duct 
height, bilinear index, first mode, 117 me. 


required to affect the S-band signal, but not until the strength is measured relative to free space value and 
layer is rather thick is the low frequency affected by it. — 33 db is standard, (s = — 3 corresponds to a value 
In the period so far studied (960 hours total) the of dM/dh about — 100/100 ft; 5 = — 2 is — 30 per 100 


16 


TRANSMISSION EXPERIMENTS OVER MASSACHUSETTS BAY 


ft, etc.) Note that for the bilinear model, unless the 
slope of the bottom portion be extreme, the duct height 
must be of order 200 ft or higher before there is any 
appreciable effect at this frequency. 

Figure 12 is a similar theoretical diagram for the 
high S-band path. The scale in this case is 0 to 100 ft. 
At X band the corresponding changes occur over a 
height range of only about 30 ft. For the low paths 



Figure 12. Theoretical field strength versus duct 
height, bilinear index, first mode, high S band. 


at any given frequency the curves are similar, but the 
increases in field strength occur more rapidly, so that 
the free space value is reached at essentially the same 
duct height for both high and low paths. 

In a few special cases for S and X bands contribu- 
tions of a number of modes (as many as 18 in one case) 
have been added in phase. In no case did the calculated 
field strength reach a value more than 15 db above the 
free space value, and in most cases it was between 
— 5 and -|-10 db. 

The calculations check well with observations in a 
qualitative way in spite of the fact that the bilinear 
curve is not in general a good approximation to the 
true M curve and that the assumption of a uniform M 
curve along the entire transmission path is an ex- 
treme idealization. They show the order of magnitude 
of duct heights at which appreciable increases in field 
strength first occur at a given frequency. They demon- 
strate also the important fact that the field strength 
is increased even at considerable heights above the 
duct. This is so because with a leaky mode the height- 
gain function does not decrease with height above the 
duct but instead becomes practically constant over an 
appreciable range. This is illustrated in Figure 13, 
where the normalized height-gain function for a leaky 
case is compared with the standard. The decrease in 
absolute value of the height gain is compensated by 
the reduction in the attenuation. It is thus clearly 
not necessary to put a transmitter inside the low duct 
in order to take advantage of it; nor does the first 
mode need to be actually trapped as indicated by ray 


tracing, but merely less attenuated than the standard. 

As to character of the signal, the theory suggests 
that steady signal is obtained with low ducts because 
only a single mode is important. With large ducts fad- 



Figure 13. Height-gain functions, standard and leaky 
first modes. (Ordinate: height. Abscissa: gain.) 


ing may be caused by interference among many modes 
which change rapidly in amplitude and phase with 
small changes in refraction. Even with very large 
ducts, for terminals well above the duct, steady signal 
might again be expected because the field strength 
there would probably again result from a single leaky 
mode, in this case not the first mode. 



Figure 14. Height-gain functions within a duct com- 
pared with standard first mode. (Ordinate: height. 
Abscissa: gain.) 


Finally, the calculations agree with observations in 
showing that even when many modes are strongly 
trapped, the field strength at a fixed point does not 


TRANSMISSION CHARACTERISTICS OF AN OVER-WATER PATH 


17 


reach the high value one might expect on the basis of 
an attenuation proportional to 1/li but rather remains 
near the ordinary free space value. This results from 
the fact that coincident with the reduction in attenua- 
tion which occurs with trapping, there is also an ap- 
preciable reduction in the height-gain function within 
the duct, as shown in Figure 14. The balance of the 
two counteretfects prevents extreme increases in field 
strengths at all ranges of practical interest for micro- 
waves. 

To sum up, the 117-mc transmission is noticeably 
affected both by thick surface ducts or substandard 
layers and by elevated superstandard layers up to 1,500 
ft altitude, which need not necessarily overhang. The 
wave theory for elevated layers is not yet sufficiently 
advanced to permit drawing definite conclusions. As 
for surface phenomena, an excellent qualitative agree- 
ment has been obtained between theoretical and ob- 
served results. There has been no indication of a need 
to revise the formula used for computing the modified 
index of refraction. 

Following presentation of this paper the following 
data were presented on a similar experiment^ made on 
an over-water path between San Pedro and San Diego, 
California. Transmitting and receiving antennas were 
at 100-ft elevation, with continuous wave transmission 
conducted from the San Pedro end of the link simul- 
taneously on 52, 100, and 550 me. The typical non- 
standard condition in this area is produced by dry air 
aloft subsiding over moist air near the sea surface. 



This gives rise to a sharp discontinuity in the index 
of refraction distribution with altitude at some eleva- 
tion above the earth. 

In analyzing the data from this experiment, the 


index of refraction modified for 4a/3, instead of the 
modified index M, was used. The new modified refrac- 
tive index, B, thus obtained is shown in Figure 15. 
The pertinent factors for reflection considerations are 
as follows : li, the height of the layer above the earth ; 
Ai?, the total change in index through the layer; and 
D, the thickness of the layer. For moderately high 
layers, D is much less than h. 

Maximum field strength measured during tlie hour 
in which a meteorological sounding was taken is 
plotted against height of the layer above the ocean. 
The data are segregated into groups for different 
ranges of change in index of refraction through the 
layer. Figure 16 shows the data for changes in Ai? 
between 30 and 40 by means of crosses ; for Ai? of 40 
to 50 with dots; and for A5 of 50 to 60 with circles. 

If reflections are assumed to take place midway 
between the transmitters and receivers, the field 
strength may vary roughly as shown in Figure 16. 
The height-gain function holds the lower frequency 
fields down when the layer is low, whereas the added 
advantage in the reflection coefficient produces rela- 
tively stronger fields for the lower frequencies when 
the layer is high. A complete report will be made soon 
on the experimental data and its relationship with 
this consideration. 

It was further pointed out that maximum observed 
field strength need not always coincide with complete 
trapping. The experimental evidence that for a given 
frequency the signal strength over a low fixed path 
first increases as the height of the base of the M in- 
version increases and then decreases does not neces- 
sarily contradict the wave guide theory. When the base 
is low, transmission is by means of well-excited modes 
with low attenuation. As the base height increases, the 
attenuation of some of the modes decreases and the 
field strength therefore increases. Further increase 
in base height results in well-locked modes which are 
more and more difficult to excite. It is then that the 
most effective mode is one which leaks sufficiently to 
be excited by a transmitter outside the duct and yet 
does not leak sufficiently to be strongly attenuated 
before reaching the receiver. As the height continues 
to increase, modes which can be excited are all strongly 
attenuated, and the ones which are only slightly at- 
tenuated cannot be excited. Thus signal strength ul- 
timately decreases with increasing height. 


LAYER ELEVATION- FEET X 10* 


18 


TRANSMISSION EXPKRIMKNTS OVER MASSACHUSETTS RAY 




• o 


LEGEND 
X A B 31 -40 

• A B 41-50 

• A B 61-60 


I- 



m 

9 

goo^o ^ 


X * 

®f8« , o 

X 

• 

X 

• 

*• • g 

ox® • 

X 


,\8» X 

2 

9 • 


• * 

vx 

!*• • 

• 

1 


52 MC 




O o 


60 


50 


40 


30 


20 


W 


• 

« 

4 

« t 




<o fii ^ .4 

< 4 % t » V* • 


•• •• A 

>f 0 xo • •• • 

C X . ».■*<> , 

{ O . • , ••• * ?. 

• *x • • 


100 MC 


cC 

o 


60 


50 


40 


30 


20 


10 


0 


X X 

e 


0^ 


• • 


Cf oo 
• 0<> 


e 

o o o 
c 

•« o 
r 


/% • 


* »- 


o o 


; o 


547 MC 


* ; •* 


• • 


1 


■fe ^0 30^ 30 20 1 0 

SIGNAL-DB BELOW FREE SPACE 




Figure 16. Signal versus layer elevation. 


Chapter 2 

TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 


2 1 ONE-WAY TRANSMISSION EXPERI- 
MENTS OVER THE SEA BETWEEN 
LOS ANGELES AND SAN DIEGO^ 

O NE-WAY TRANSMISSION tests liave been made by 
two methods : over a fixed path and by means of 
an airplane to sample vertical distribution of field 
strength. The fixed path is a nonoptical over-water 
path, 80 nautical miles in length from San Diego to 
San Pedro near Los Angeles Harbor. No intervening 
landscape is present at either end of the path. The c-w 
transmitters are located at the San Pedro end of the 
path at 100-ft elevation and operate on frequencies 
of 52, 100, 547, and 3,200 me. The latter frequency 
has just recently been added, and insufficient data 
have been obtained to include in this report. The trans- 
mitters are quite conventional, the 52 me being crystal 
controlled and the other two being self-excited units 
in which adequate frequency stability has been ob- 
tained by use of high-Q circuits. Monitors, which are 
read periodically, are provided on each transmitter. 
The receiver location, at 100-ft elevation, is located 
on Point Loma, San Diego, near the laboratory. The 

®By L. G. Trolese, U. S. Navy Radio and Sound Labo- 
ratory, San Diego, California. 


receivers are of standard construction incorporating 
a balanced d-c amplifier and Esterline- Angus recorder 
in the output circuit. Filament and plate voltages are 
regulated. Detuning effects due to temperature changes 
are minimized by temperature regulation in the re- 
ceiver house. Receivers are calibrated at least once 
each week. 

Four receivers have been installed in a PBY-5A 
plane which is used to sample vertical sections of field 
strength distribution at various distances up to 130 
miles from the transmitters at 100-ft elevation. The 
frequencies used are 63, 170, 524, and 3,250 me. 
Certain precautions were found necessary to insure 
correct orientation of transmitting antennas on the 
ground and receiving antennas on the plane. Receiving 
antennas on the plane are fixed in position, and meas- 
urements are taken only with the plane flying toAvard 
the transmitters. The plane’s orientation is controlled, 
and the distance from transmitters determined, by 
utilizing the plane’s Type ASF (Admiralty Signal Es- 
tablishment) radar to home on a beacon located near 
the transmitters. All four transmitters and transmit- 
ting antennas are installed on a single rotating moimt. 
A direction finder system also installed on the rotat- 
ing assembly and operating on the plane’s radar fre- 



Figure 1. Maximum received signal versus atmospheric refraction. 


19 


20 


TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 


quency is used to check the plane’s bearing during 
flight and keep the transmitting antennas pointed at 
the plane. Bearing checks have been consistently ob- 
tained at ranges up to 130 miles. The d-f bearings 
agree quite well with those obtained by use of a type 
FC Are control radar. 

One-Way Fixed Link Data 

Ray Theoky — Geometkic Optics 

On the basis of ray theory, when it is assumed im- 
plicitly that the energy follows the rays, the modified 
index criterion for trapping should be expected to 
agree with experience. Ray tracing theory states that 
when the modified index at some elevation above a 
transmitter attains a value equal to or less than its 
value at the transmitter height trapping can occur. 

As a preliminary check on this criterion the maxi- 
mum field strength observed during the hour in which 


below detection for all the frequencies used on the 80- 
mile over-water link. This has been confirmed experi- 
mentally. On November 5, 1044 a front passed accom- 
panied by heavy rain which dissipated all low-level 
inversions, and a standard condition resulted. During 
this period all the signals decreased below detection. 

Figure 2 shows the above field strength data plotted 
against the height of the base of the temperature in- 
version. (The curves appearing in this figure will be 
explained later.) Although both the thickness of the 
inversion layer and the strength of the inversion vary 
considerably, the correlation of signal strength with 
the height of the base of the inversion is quite remark- 
able. The 547-mc signal decreases below detection as 
the layer heights increase above 3,000 ft ; whereas the 
100- and 52 -me signals are still relatively strong when 
the inversion base is above this altitude. These lower 
frequencies do show a decreasing trend as the layer 
continues to rise, going completely out, as stated above, 
when the low-level inversion is washed out. 




Figure 2. Maximum received signal versus altitude of base of temperature inversion. 


the meteorological sounding was taken is plotted 
against AM in Figure 1. When the minimum value 
of M in the refracting stratum is less than its value 
at the transmitter elevation, AM is negative, and the 
trapping condition is fulfilled. The 52-, 100-, and 547- 
mc links all show strong fields for large positive AM. 
These data are not compatible with the assumption 
that the energy follows the rays. The diffracted field is 


Figure 3 shows a condensed log of the field strength 
data taken on the one-way link. Maximum and mini- 
mum field strengths during successive 2-hour intervals 
are plotted, thus showing the general level and fading 
range for each frequency during a 6-week period. The 
corresponding elevation of the base of the tempera- 
ture inversion is shown by the discrete points in the 
upper part of Figure 3. It is at once apparent that the 


ONE-WAY TRANSMISSION EXPERIMENTS OVER THE SEA 


21 


signal level is higher for all frequencies when the layer 
is low and also that the fading range is smaller under 
these conditions. For a given elevation of the layer the 
fading range is greater for the higher frequencies. 

Figure 4 shows the character of the signal received 
on the one-way link when the inversion was low and 
trapping was definitely indicated by the modified in- 


ing layer above the earth. The degree of trapping 
depends upon the number of modes, or eigenvalues, 
allowed under the given boundary conditions. 

The San Pedro to San Diego continuous transmis- 
sion link yields data which can be compared with the 
simple wave guide theory. The 52-mc data are of par- 
ticular interest, since for this frequency no meteoro- 


80 MILE LINK SAN PEDRO TO SAN DIEGO 
TRANSMITTER AND RECEIVER AT 100 FT. ALTITUDE 




BASE OF TEMPERATURE INVERSION 

• o* 


1-4000 


•o.V.- 

» • O 


• • • • 

• 

^ • o 




• 




•• a m 


«• • 



SFPTEM BER OCTOBER 

Figure 3. Maximum signal and fading range related to height of base of temperature inversion. 


dex curve. Figure 5 shows the signals under the con- 
dition of a high inversion. The time scale is shown 
along the horizontal at the top of 547 -me tape and at 
the bottom of the 52-mc record. For the condition of 
a low layer and strong trapping the level of all the 
signals is high and the lower frequencies are quite 
steady. As the elevation of the layer increases the 547- 
nic signal decreases below detection, the lower fre- 
quencies become less steady and the maximum level 
decreases. Figure 5 in contrast with Figure 4 clearly 
demonstrates this situation. 

Wave Guide Theory 

According to the simple wave guide theory, using 
the modified index, trapping can occur only when 
Ad/^O; and then only when the wavelength is suffi- 
ciently small compared with the height of the reflect- 


logical data have been taken which would indicate any 
modes allowed. Yet the field strength has varied over 
a range of some 30 db, the strongest fields occurring 
at times of high fields on the 547- and 100-mc links. 

Figure 6 shows the variation of the maximum field 
strength of the 547- and 100-mc frequencies versus 
the number of modes allowed as calculated from the 
meteorological data. There is no apparent correlation 
at either frequency. 

Reflection Theory 

It has been shown theoretically^ that reflection from 
a nonhomogeneous stratum may occur, even when both 
the index of refraction and its gradient are continu- 
ous functions through the layer. The controlling fac- 
tor, for a given incident angle, is the ratio of the 


22 


TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 


stratum thickness to wavelength, I)/\. At normal 
incidence the reflection coefficient is small, even for 
however, such reflections have been ob- 
served experimentally.^ At oblique incidence, for the 



Figure 4. Signal types on one-way link for low in- 
version (trapping). 


cases where the index of refraction varies monotoni- 
cally through the layer, the reflection ratio increases 
as D/\^0. For the modified index type the reflection 
ratio increases as D/X decreases, passing through a 
maximum after which it again decreases.^ 

Figure 7 shows the reflection ratio as a function of 
D/X for various angles of incidence, where here the 
index of refraction is a monotonically decreasing func- 
tion of height through the layer. The total change in 
n through the layer is taken to be 60 X 10"^^ which is 
the order of magnitude of the changes noted in this 
area during the summer season. For a given stratum 
thickness and height above the earth such that the 
radiation will be incident upon the layer at angles 
slightly less than the critical angle, the lower fre- 


quencies will be reflected more strongly from the 
layer. In addition, any deviation of the layer from 
the horizontal plane will affect the higher frequency 
radiation more than the lower frequencies. This is 
manifested by the greater fading range of the 547- 
nic signal as shown in Figure 3. 

Consider the case where the layer is 330 ft thick. 
Since the angle at which the radiation will be inci- 
dent upon the layer will depend upon its elevation, 
it is possible to compare the experimental data with 
theoretically calculated reflection ratios. In Figure 2, 
the curves indicate the theoretically predicted varia- 
tion of field strength as the layer rises. The absolute 
decibel scale does not apply to the theoretical curves; 
only the slope is significant. The actual layer thick- 
ness and the effective change of the index of refraction 



Figure 5. Signal types for high inversion. Note the 
low level of the 547-inc signal. 


through the layer varied around the values used, and 
so an exact correspondence between theory and experi- 
ment should not be expected. However, the agreement 
is fair. In addition, at any given time the reflecting 
stratum is a warped surface which changes shape with 



ONE-WAY TRANSMISSION EXPERIMENTS OVER THE SEA 


23 


time. This condition complicates any theoretical treat- 
ment of the problem. 

The analysis thus far indicates that the variation in 




-30 -20 -K) 0 

OB ABOVE FREE SPACE 


Figure 6. Number of modes trapped. 

actual index of refraction through the layer has to 
be used to explain the magnitude of the fields observed 
on the one-way link. When the layer is thin the longer 



Figure 7. Reflection ratio. 


wave radiation might be expected to leak more readily 
through the stratum and thus show less trapping at 
the greater distances. Actually, the vertical sections 
of field strength taken in the plane (Figures 8 and 9) 


show rather large fields above the layer at the longer 
ranges. This might be interpreted in favor of the 
modified index over the measured index of refraction. 
However, on the other halid it could be diffraction due 
to the low elevation of the layer, or a storage field when 
the actual index of refraction is used. A study of the 
attenuation along the path should clear up this last 
point. 


2.1.2 Vertical Field Strength Sections 

Two typical sets of field strength data are shown 
in Figure 8 and in Figure 9. Figure 8 illustrates a 
case for which there was definite trapping predicted 
by the modified index criterion. It will be noted that 
the 63-mc radiation shows little variation in field 
strength with altitude. In most cases it shows even 
less variation with time at a given altitude. The higher 
frequencies show more variation of signal with alti- 
tude, and the field strength distribution varies more 
with time. This variation with time is in complete 
agreement with the data taken on the San Pedro to 
San Diego one-way link. The minimum field above the 
minimum point of the M curve, as predicted by ray 
theory, is certainly missing at the lower frequencies 
and rather uncertain at the higher frequencies. 

Figure 9 in the following paper shows field strength 
sections for a day when the reflecting layer was at an 
elevation of around 3,000 ft. Here the solid line rep- 
resents the first run and the dotted line the repeat sec- 
tion. The time interval between sections was from an 
hour to an hour and a half. The sections at about 75 
miles from the laboratory show results compatible with 
the one-way link data. At low elevations the lower 
frequencies show stronger fields than the higher fre- 
quencies. This again is in agreement with reflection 
theory. 

Summary 

The modified index of refraction, in conjunction 
with ray theory, is a poor criterion for trapping. 
Strong fields are observed well below the horizon when 
the observed modified index would indicate that no 
trapping would be taking place. The vertical distribu- 
tion of field strength for the lower frequencies appears 
to have little in common with the fields predicted by 
ray tracing methods Avhere the energy is assumed to 
follow the rays. 

There is no apparent correlation between the experi- 
mental data and the simple wave guide analysis. 


GEOMETRIC TANGENT 


24 


TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 



0«o^K)cg*0 — o K><g — O 


g.oi * ij Ni sonxinv 


Figure 8. Vertical field strength sections. Transmitter at 100-ft elevation. Date: October 2, 1944. 


ONE-WAY TRANSMISSION EXPERIMENTS OVER THE SEA 


25 



26 


TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 


Treating the elevated refracting stratum as a plane 
reflecting layer seems to agree in general with experi- 
ence, for the following reasons. (1) The observed fre- 
quency sensitivity of the reflecting layer is predicted. 
(2) The observed fading characteristics of the differ- 
ent frequencies is again in the right direction, the 
higher the frequency the greater the fading. (3) 
Strong fields well below the horizon under conditions 
of high layers cannot be explained on the basis of 
refraction alone. 

2 2 the CORRELATION OF CALCULATED 
AND MEASURED FIELD STRENGTHS'^ 

Since the time of issue of reference 3, the impor- 
tance of further experimental check against the cal- 
culated patterns has been fully realized. 

The field strength cross sections recently obtained 
by airplane-borne receivers have made possible such 
a check. 

For anything more than a rough qualitative corre- 
lation it was soon apparent that quantitative field 
strength analyses were needed for the actual observed 
meteorological conditions. 

Because of the clearly apparent influence of high 
level inversion layers on the observed radiation fields, 
this type of condition was selected. Consider, for ex- 
ample, the M curve at 50-mile range obtained on 
September 29 reduced to three linear segments as 
shown in Figure 9.® It is clear that the M curves at 
10 and 100 miles are not seriously different. 

We thus have a condition in which M — Mq de- 
creases by 50 units in a 200-ft interval of altitude 
attaining the minimum value of -1-50 at 3,000-ft 
elevation. 

Figure 10 shows the ray diagram constructed for 
the analysis. The diagonal lines below 4,000 ft rep- 
resent the positions at which field strengths were 
measured and calculated. 

The actual size of the ray diagrams is 27x40 in. 
Rays in the region of standard refraction have a 58-in. 
radius. Through tlie transition layer the radius is 4 
in. The a])ove radii are determined by the vertical and 
horizontal scaling factors and are approximately one 
ten millionth of the curvature as given by dM/dh. 
Note that the downward curvature of the earth and 


'’By F. R. Abbott, U. S. Navy Radio and Sound Labo- 
atory, San Diego, California. 

®See discussion of Figure 9 in Section 2.1.2. 


upward curvature of rays in the standard propaga- 
tion regions are made equal, thus reducing the slopes 
of the rays and resulting errors inherent with de- 
formed scale graphical methods. 

Since the tangent ray (shown with short dashes) 
intercepts only a small part of the fourth and none 
of the fifth section of measurements, the analysis 
methods employed in radar coverage diagrams had 
to be extended. Specifically, the coverage diagram 
analysis at NRSL has applied to fields between 85 and 
100 db below that at a distance of one meter from the 
transmitter. This largely excludes consideration of 
any but interference and trapping zones. 

The measurements with which correlation was de- 
sired extended to about 30-db weaker fields so that 
partial reflection and diffraction fields were involved. 

Proceeding with the ray tracing analysis, the in- 
terference field was calculated at points of intersec- 
tion of the direct and sea-reflected rays. Path differ- 
ences were determined using a map measure and a 
planimeter as explained in reference 4. Ray densities 
were measured for the direct and reflected compo- 
nents, and the associated fields were added with re- 
spect to the phase. The diffraction field below the 
tangent ray was calculated by Norton’s method. 

Reflected rays from the layer were introduced as 
originating at the center of the layer. The reflection 
coefficients for the angles of incidence were calculated 
as described in reference 5 for the case of a mono- 
tonic transition layer in Avhich the refractive index 
decreases by 50 X 10~'\ In the terms of field intensity 
the reflection coefficient values ranged from 0.2 to 
0.1 at 63 me and from 0.01 to 0.003 at 524 me. 

In Figure 9 the calculated normal interference 
and diffraction fields are shown dotted beside the 
measured values except at 3,250 me on which the 
30- and 45-mile sections have been displaced for 
clarity. At 63 me there is an apparent displacement 
of about 3 db which is probably associated with the re- 
duction in measurements to the decibels below the field 
at a distance of 1 m from the transmitter. Note that 
at 60 miles the interference pattern of the diffraction 
and partial reflection fields as calculated appears with 
a phase displacement of about 180 degrees from the 
observed field. The phase relationship depends, of 
course, on an assumed value of 90 degree change of 
phase on reflection. 

At 170 me there is a displacement of about 10 db 
due to difficulty of reduction in measurements. In- 
troducing a 10-db correction, all values at 170 me 


THE CORRELATION OF CALCULATED AND MEASURED FIELD STRENGTHS 


27 



133J Nl 1H0I3H 


Figure 10. Ray diagram 20. M curve 30,2,50. Antenna height 100 ft. 


28 


TRANSMISSION EXPERIMENTS NEAR SAN DIEGO 


agree closely, including the field at 130 miles, due 
solely to partial refiection. No attempt was made to 
calculate the detailed variation with altitude. 

The agreement between calculated and observed 
fields at 524 me is excellent above, but poor below, the 
tangent ray. At 130 miles 20- to 30-db difference ap- 
pears. Note that the measured field is about 20 db 
greater than the 170-mc field at that range. This 
contradicts the trend of the calculated refiection coef- 
ficients which should decrease exponentially with rela- 
tive thickness of the layer measured in wavelengths. 
The observed 524-mc fields at 130 miles on some other 
days of pronounced high-level inversions were well 
below the 170-mc fields and thus in qualitative agree- 


ment with theory. At 3,250 me there is again good 
agreement above the tangent ray, but again, in the 
region below, the observed fields were high though the 
calculated values became very small. 

Thus a preliminary check of analysis versus meas- 
urements indicates: 

1. Discrepancy of absolute values except where the 
field at the maximum of a lobe was measured. 

2. Excellent agreement as to variation with range 
and altitude above the geometric tangent as well as 
in the diffraction-partial refiection zone, except that 
at 524 me and 325 me strong fields were observed 
below 4,000 ft to 130 miles in contradiction with 
theory. 


I 


Chapter 3 

TRANSMISSION EXPERIMENTS IN ARIZONA 


3 1 ATMOSPHERIC REFRACTION UNDER 
CONDITIONS OF A RADIATION 
INVERSION^ 

A n investigation of propagation of high-frequency 
- radio waves under conditions of a nocturnal tem- 
perature inversion was made in Arizona over a short 
period in December 1944. Climatic conditions in this 
region permitted testing the dependency of refractive 
index in the lower troposphere on the temperature 
lapse rate, since the water vapor content was expected 
to remain relatively constant. 

During the day in this area the soil heats rapidly, 
producing vertical instability and convection mixing 
near the ground and hence a temperature lapse rate 
in the lower atmosphere approaching the dry adia- 

“By J. B. Smyth, U. S. Navy Radio and Sound Laboratory. 


batic rate. After sunset the soil temperature drops 
rapidly, cooling the layer of air adjacent to the sur- 
face and producing a low-level radiation inversion 
during the night. 

It was thought that the progression of this low- 
level inversion would at times cause the lapse rate of 
refractive index to vary between slightly positive and 
zero, which would be the case of greatest interest. If 
during such a variation of lapse rate field strength 
observations are made with a receiving antenna which 
under standard conditions is in the earth shadow re- 
gion, a test can be made of Hoyle’s hypothesis^ that 
temperature lapse rate is of greater significance than 
is now believed. If, for exalhple, the field strength 
during one-way transmission reaches the value cal- 
culated for a fiat earth while the modified refractive 
index lapse rate is still positive, then something must 
be wrong with either the modified index concept or 



29 


30 


TRANSMISSION EXPERIMENTS IN ARIZONA 



14 16 Id 20 22 24 02 04 06 08 lO 12 14 16 18 20 22 24 02 04 06 08 10 

DECEMBER 16 


Figure 2. Soil and air temperatures at Datelan, December 16 to 17, 1944. 


the method of calculating refractive index from mete- 
orological data. 

When the modified index lapse rate is relatively 
constant with altitude, a fairly simple transformation 
makes the atmosphere nonrefracting and the effective 
earth radius greater or smaller than the actual radius, 
and ray tracing should then be valid in the interfer- 
ence field. If no rays reach the receiver, the diffracted 
field must supply all the energy received. 

The propagation path extended from Datelan to 
Gila Bend, Arizona, a distance of 47 miles over desert 
terrain. A 3,200-mc transmitter was located on a tower 
at a height of 53 ft above ground at Datelan, with the 
receiver 35 ft above the ground in the control tower 
at the Gila Bend airfield. There is a gentle rise of 
ground from Datelan to Gila Bend with a total rise 
in elevation of 402 ft, or about 8.5 ft per mile. The 
intervening terrain is remarkably uniform, without 
trees or large irregularities, and there are no build- 
ings except in the immediate vicinity of the trans- 
mitter and receiver locations. 

Figure 1 shows the diurnal variation of surface air 
temperature at A jo, Gila Bend, and Phoenix for 
December 16 and 17, 1944. These typical data show 
the uniformity of conditions over that region and 
the effect of radiation cooling on the air mass near 
the surface. 

Figure 2 shows the variation of the soil tempera- 


ture with time at Datelan for the same period, as well 
as temperature changes at 25, 50, 100, and 500 ft 
above the earth. 

The general topography around Gila Bend in con- 
junction with the diurnal variation in the prevailing 
surface wind vector shows an interesting condition. 
Hourly wind vector observations during November 
and December 1944 showed that by 1900 the prevail- 
ing wind was downslope toward the lower elevations. 
This flow of cold air into the area of the link may be 
responsible for the overall cooling of the air up to 
several hundred feet during the night. At present it 
is not clear how much of this effect should be attrib- 
uted to radiation and eddy diffusion of heat toward 
the earth, although on nights with wind speeds from 
calm to a gentle variable breeze it is difficult to at- 
tribute the entire transport of heat to the latter 
processes. 

Some pertinent data are tabulated in Table 1 show- 
ing the time at which the signal was first detected and 
completely lost and the general atmospheric and 
ground conditions nearest these times. On the after- 
noon of December 14, the sky was overcast, and the 
signal was detected about an hour earlier than on the 
other evenings. 

Figure 3 shows the field strength data for a typical 
day plotted in decibels below free space. The maxi- 
mum and minimum for half-hour intervals are shown 


REFRACTION UNDER CONDITIONS OF RADIATION INVERSION 


31 


Table 1 


Date 

Time 

of 

sunrise 

Signal 

below 

detection, 

time 

Cloud condition 

Soil 

temperature 

Time 

of 

sunset 

Signal 

first 

detected, 

time 

Cloud condition 

Soil 

temperature 

12/13 

0653 




1655 


Few cirrus 

1800 

13C 

12/14 

0654 

0845 

0800 

Clear 

0800 

3.1C 

1656 

1615 

1730 

Overcast 

Altostratus 

Cirrostratus 

2000 

9.0C 

12/15 

0655 

0945 

0800 Scattered low clouds 
Scattered middle clouds 
Scattered altostratus 

0800 

2.0C 

1656 

1715 

1600 

Scattered cirrus 

1700 

19.4C 

12/16 

0655 

0925 

0800 

Overcast 

High cirrus 

0900 

6.4C 

1656 

1725 

1700 

Scattered cirrus 

1700 

19.3C 

12/17 

0656 

0940 

0900 

Scattered cirrus 

0900 

5.3C 

1656 

1730 

Few cirrus 

1700 

17.9C 

12/18 

0656 

0950 

0900 

Clear 

0900 

6.0C 

1657 

1738 

1700 

Scattered cirrus and 
altostratus 

2000 

8.5C 

12/19 

0657 

0923 

0900 

Clear 

0900 

8.8C 

1657 

1628 

1700 

Scattered cirrus 

1630 

20.8C 

12/20 

1658 

0910 

0900 

Clear 

0900 

8.7C 

1658 






Figure 3. Typical field strength and modified index curves, December 16 to 17, 1944. 


32 


TRANSMISSION EXPERIMENTS IN ARIZONA 


so that the fading range is apparent. The meteorologi- 
cal data for the period are given in the form of modi- 
fied refractive index curves relative to a fictitious earth 
radius of 4a/3, the time of the sounding being given 
on each curve. 

The diurnal variation in field strength is quite pro- 
nounced and regular. The maximum range of fields 
measured was around 46 db, the maximum field gen- 
erally occurring at times when the inversion layer was 
thickest. There is no significant correlation between 
strong fields and the amount that M decreases at some 
elevation above the antennas. In fact, at times such 
as 0900 on December 17 the field strength is quite 
high and yet M shows little indication of trapping. 
In most cases strong fields occur at times when the 
4a/3 modification of the index of refraction gradient 
is near zero or varying slowly with altitude. 

The general results of this experiment may be sum- 
marized in the following way. Over the desert loca- 
tion a ground-based temperature inversion was found 
each night due to radiation cooling of the under- 


lying surface. This temperature inversion produced a 
strong index of refraction gradient in the first few 
hundred feet above the earth. 

The 10-cm nonoptical link showed a marked diur- 
nal variation in field strength in close correlation 
with the building up and intensification of the tem- 
perature inversion. The strongest fields generally ac- 
companied modified index gradients approaching zero 
in the first few hundred feet above the earth’s surface. 

The trapping criterion most widely accepted here- 
tofore specifies that, at some elevation above the 
transmitter and receiver antennas, M should be less 
than at the antennas. The data herein reported seem 
to indicate that this criterion is neither necessary nor 
sufficient to insure strong fields below the optical 
horizon. The strongest fields observed at 10 cm ap- 
proached the fiat earth value, assuming a reflection 
value of unity for the earth.^ 


‘’Section 5.4 will be of interest in connection with this 
chapter. 


Chapter 4 

TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


4 1 PROPAGATION IN S AND X BANDS 
IN LOW-LEVEL OCEAN DUCTS 

General Description® 

T he existence of low-lying ducts over the seas of 
the world, particularly in the trade wind belt, has 
been known for the past 2 years. Measurements made 
by the British and by Washington State College and 
the Naval Research Laboratory have consistently in- 
dicated the presence of ducts ranging in thickness 
from 20 to 50 ft in regions where the trade wind 
followed a long over-water trajectory. These ducts 
are known to vary in intensity and thickness with 
wind velocity during the trade wind season. It was 
considered advisable to investigate the possibility 
that such ducts would permit greatly extended ranges 
on surface craft and very low-flying aircraft by prop- 
erly sited radar installations. 

Discussion by representatives of the Chief of Naval 
Operations, NDRC, and the Naval Research Labora- 
tory resulted in organization of a project to make an 
experimental investigation of meteorological and prop- 
agational conditions in an area of the Caribbean 
theater where siich ducts are persistent, with a view 
to determining their operational usefulness. It was 
decided that a one-way ship-to-shore transmission 
path over water would provide the most direct data 
for analysis, and such a system was set up, using 
transmitting and receiving equipment provided by 
the Radiation Laboratory. The transmitters were in- 
stalled in a patrol craft assigned for the project, there 
being no larger vessel available, with transmitting an- 
tenna heights of 16 and 46 ft. 

The site chosen for the receivers at the land-based 
end of the link was at Judge Bay on the island of 
Antigua in the Leeward Island group of the British 
West Indies. Antennas were installed on a tower 50 
ft from the water’s edge, at heights of 14, 24, 54, and 
94 ft, for both S- and X-band receivers. 

Antennas for both S- and X-band transmitters were 
installed on the patrol craft at heights of 16 and 46 
ft. These consisted of parabolic reflectors arranged 
to permit transmission forward or astern, so that 

*By Lt. R. W. Bauchman, U. S. Naval Research Labora- 
tory. 


transmissions could be made on both the outward 
and inward legs of the runs. The S-band transmitter 
peak power output was 42 kw, and its antenna pro- 
vided a measured gain of 27 db. Output on X band 
was 31 kw, the antenna providing a measured gain 
of 29 db. Later in the experiment an S-band antenna 
was installed at a height above the water of 8 ft. 
Tests were made with this antenna on two runs. Ad- 
equate switching arrangements to permit tests with 
the different antennas were provided, and power out- 
puts were measured by means of directional couplers 
and thermistor bridges. 

Meteorological measurements from the ship con- 
sisted of detailed temperature and relative humidity 
readings taken on a rigging running from a boom 
extending out over the water amidship to the yard- 
arm about 46 ft above the water. Low-level sounding 
equipment of Washington State College design was 
used for all meteorological measurements. Balloon 
ascents to heights of 600 ft from the stern of the ship 
were also made when conditions permitted. Hourly 
observations of sea temperature, wind, and sling psy- 
chrometer readings from the bridge were made. It was 
impossible to obtain satisfactory soundings on the 
rigging or by use of balloons and kites when running 
away from the tower into the wind because of the 
large amount of water taken over the bow and the 
resulting salt spray. Shipboard observations during 
outward runs were therefore confined to the hourly 
wind velocity, sea temperature, and sling psychrom- 
eter readings. On return runs with the wind, bal- 
loon and rigging soundings were made. It was neces- 
sary to estimate the height above the surface for 
readings taken below 10 ft because of the severe 
pitching and rolling motion of this type of ship, and 
therefore very few such readings were made. 

At the receiving end of the radio path, the antennas 
for S band were 48-in. parabolic dishes with a gain 
of about 30 db. The X-band antennas were 48-in. 
dishes cut to 2 ft in the horizontal dimension to 
broaden the horizontal acceptance angle. This was 
done to eliminate the effects of minor deviations of 
the ship from a radial course. These antennas had a 
measured gain of 35 db. Midway in the experiment 
an X-band antenna was mounted at the base of the 
tower at a height of 6 ft, since results up to that 


33 


34 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


time indicated the lowest available antenna height 
on X band gave the strongest signals. All antennas 
were mounted on swivels to allow alignment on any 
course over a 40-degree arc and were connected by wave 
guide and stub-supported coaxial cable. 

Two S-band and two X-band receivers feeding 


stability of tlie 8-haiid magnetron. The receivers were 
calilu’ated with standard test sets before every run 
and checked upon the completion of each test. Indi- 
vidual calibration curves were then used in plotting 
the results of each run. Since only two receivers on 
each band were available, an r-f switching arrange- 



20 40 60 80 100 120 140 160 

Figure 1. S-band run out, March 19 to 21, 1945. Signal strengths of various antenna coinbinations compared to free 
space level. 


Esterline-Angus recording milliammeters were kind- 
ly furnished by the Radiation Laboratory. The S- 
band receivers had a minimum sensitivity of 110 db 
below 1 w, while the X-band receivers had a mini- 
mum sensitivity of 105 db below 1 w. It was necessary 
to use automatic frequency control on the X-band 
receivers, but manual tuning was employed on the 
S-band receivers because of the greater frequency 


ment similar to that used on the ship was employed. 

Two-way voice communication between the ship 
and shore station Avas maintained at all times for 
coordination of operations. The facilities of an Army 
radio direction-finding station on the island were 
available to obtain bearings on the ship. 

Meteorological measurements were made at the 
shore station during operations by means of kite 


PROF’AGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


35 


fliglits and a guy rigging running from the water’s 
edge to 10 ft above the top of the tower. Detailed 
soundings in the first 100 ft Avere then taken by slid- 
ing the measuring instruments up and down the 
rigging. Since the duct conditions important in this 
investigation Avere ahvays beloAV 100 ft, only occa- 


A typical jArocedure Avas to align tlie ship at a point 
about (i miles off shore (closer ranges Avere impossible 
because of reefs lying off the northeastern coast of 
the island) and commence a run on a prescribed 
bearing aAvay from the toAver. This bearing Avas pre- 
determined by ship observations of the current Avind 



Figure 2. S-band run in, March 19 to 21, 1945. Signal strengths of various antenna combinations compared to free 
space level. 


sional kite soundings (two to three a day) Avere made 
to check the higher levels. Most of the data accumu- 
lated were taken on the toAAw rigging AA^here detailed 
soundings could be made. Wind speeds at the surface 
and 100 ft levels Avere recorded hourly. Hygrother- 
mographs Avere placed at the antenna levels and con- 
tinuous records taken to determine the diurnal varia- 
tion of temperature and relative humidity, if any. 


and sea direction. The receiving antennas Avere 
aligned to maximum signal strengths recorded by the 
receivers and secured in this position by clamping to 
the deck. The ship operating speed Avas usually around 
10 knots, depending on the current sea conditions. 
While the ship Avas moving on the course, antenna 
changes on the receivers Avere made every 15 minutes 
for some runs, Avhile antenna heights on the trans- 



36 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


mitting end were changed every 2 hours. After making 
several runs using this procedure, results showed that 
there was no discernible diurnal variation of signal 
strength. Therefore, later runs were made using an- 
tenna changes on the transmitting end only at the 
conclusion of the run out. Periodic changes of the 


X-band antennas was realigned to give maximum 
signal return and the change in ship’s bearing noted 
by use of a bearing marker attached to the antenna. 
This change was then applied to the remaining an- 
tennas and the ship’s course changed accordingly. 
Additional checks on the ship’s course were obtained 



Figure 3. X-band run out, March 19 to 21, 1945. Signal strengths of various antenna combinations compared 
to free space level. 


receiving antenna heights were made in order to 
obtain a complete record of all possible antenna com- 
binations during each run. 

One of the main difficulties encountered in this 
type of operation was keeping the ship on the sched- 
uled course. Deviations from this course were detected 
by means of sudden drops in signal strength on the 
X-band receivers. When this occurred, one of the 


by means of the radio direction-finding station. By 
using this information, it was possible to detect de- 
viations in the ship’s course without losing any part 
of the record. The ranges of these runs extended up 
to a maximum of 190 miles. Signals were usually 
detected out to this range on the lowest X-band com- 
bination and the highest S-band combination of trans- 
mitting and receiving heights. 


PROPAGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


37 


Figures 1, 2 , 3, and 4 show the plots for one com- 
plete run. It is apparent that the lower antenna com- 
binations on X band produced the highest signal level. 
Signal strengths from higher antenna combinations 
declined proportionately with height. On S band the 
reverse appeared to be true, the 46- to 94-ft antenna 


tion. This clearly shows that the highest combination 
available with this setup produced the best results. 
It can also be seen that the signal level is considerably 
further below the free space value than is the X-band 
signal for these ranges. 

In order to determine the effect on the signal 




















































































1 


































1 






























































































































>0 










X BAND IN 

MARCH 19-21 

Tronsmitter Powers 3.1 xlO^Wofts 


















A 

A 



























\ 

X. 

\ 


























\ 





























N 







































b 


\ 






































\ 



















i 
























\ 




V 


































\ 



s. 

o 



\ 













1 




















s 




\ 















FR 

EE SPACE LEVE 

K 







1 J 1 « 1 1 1 1 * r — 1 1 1 1 

RECEIVED POWER, db BELOW 1 WATT 

1 









L 



\ 



































\ 

\ 


fl 




















\ 















\ 


V 


V 




















s 
















V 























V 

N 













\ 


,\ 


\ 


































\ 



\ 
























s 













o 

\ 


V 





































5 

\ 

\ 


































V 




< 





✓ 

> 



N 






























V- 



0 

0 





N 





























\ 










\ 

























\ 




< 

\ 

/ 






. 0 

.. 

X- 

V- 



Q_ 





















\ 





/ 





o 




-o 



\ 






































Q 

• 



































\ 




k 




















\ 


























- 

LEGEND 






1 
















\ 

n 


\ 







46- 

46- 

94 
























^ • 



\ 






24 








s. 















' 



V 






46* M 
46-6 









V. 

\ 
















i! 

N 


V 































V 

\ 

b 
































\ 







































o. 











































1 











































































































































RANGE IN MILES 

















































I I I I ,, 1 , I I I I I I I I I I I I I I I I I 

20 40 60 ■ 80 100 120 140 160 


Figure 4. X-band run in, March 19 to 21, 1945. Signal strengths of various antenna combinations compared 
to free space level. 


combination giving the highest average signal level. 

Figure 5 shows a composite presentation of 16-ft 
transmitting antenna to 14-ft receiving antenna. The 
average received signal with this antenna combina- 
tion is 5 to 10 db below the 8- to 6-ft X-band antenna 
combination. 

Figure 6 is a record of all the runs on the 46-ft 
transmitting and 94-ft receiving antenna combina- 


strength of moving the antenna inland, a mobile unit 
consisting of an X-band receiver, test set, recorder, 
and 18-in. parabolic dish were mounted in a truck 
and operated from a gasoline-driven generator. Meas- 
urements during several runs were recorded V 2 , 
and 1 mile inland from the tower. The antenna heights 
above the sea surface were 25, 50, and 100 ft, respec- 
tively. In one instance, the unit was placed behind a 



38 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


hill with the antenna several feet below the top to 
see if transmission over the hill was possible. There 
was a noticeable decrease in signal strength, approxi- 
mately 13 db, but some signal was still recorded. 

Meteorological measurements were taken simul- 
taneously with the inland radio measurements. Kite 


similar to those found on the windward side of the 
island existed. 

During the final phases of the project, an X-band 
radar was installed at the base of the tower with an 
antenna height of 6 ft. Measurements of echo strength 
versus range were made on the PC boat to evaluate the 



soundings at several points at increasing distances 
inland from the water’s edge were made, and detailed 
soundings on a 50-ft windmill tower about mile 
inland were recorded over a 12-hr period. 

Additional meteorological measurements from the 
ship on the leeward side of the island were made to 
determine if duct conditions existed in this area. 
Measurements taken from 2 miles out to approxi- 
mately 20 miles off shore showed that duct conditions 


effect of the duct on X-band radar. Antenna heights 
of the radar were varied from 6 ft to approximately 
90 ft by placing the installation on the truck in much 
the same manner as was done with the receiver in the 
one-way experiment. This was then set up on sites 
overlooking the coastline to sea. The heights at which 
signal strength versus range measurements were made 
were 6, 15, 50, and 90 ft. The variation in the range 
of sea clutter for these heights was also observed. 


PROPAGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


39 


Measurements on the leeward side of the island were 
also made with this radar with approximate antenna 
heights of 6, 10, and 75 ft above sea level. 

The maximum range obtained using the PC boat 
as a target with a broadside aspect was 47 miles. This 
range was observed with the radar antenna at the 
6-ft level. The maximum range obtained on the ship 


significant radar datum obtained to leeward of the 
island was the detection of a ship at 45 miles from 
a 75-ft site. 

4.1-2 Meteorological Measurements^ 

The description of the meteorological measure- 
ments in connection with the experiment at Antigua 



is divided into three parts, as follows: first, a brief 
general description of the West Indian climate; sec- 
ond, a survey of the low-level soundings; and third, 
a necessarily hurried analysis of the data, with certain 
tentative conclusions. 

The most noteworthy feature of the climate at 
Antigua during the late winter is the persistence of 


from the 90-ft level was 26 miles. Sea clutter was 
found to vary with the antenna height and wind speed. 
Maximum return of 15 miles on sea clutter was ob- 
served at the 6-ft level with wind speeds of 20 to 30 
knots. The maximum range at which sea return was 
obtained varied proportionately with height up to 
the 90-ft level. This range was decreased 50 per cent 
with lower wind speeds of 10 to 15 knots. The most 


Lt. W. Binnian, U. S. Naval Research Laboratory. 



40 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


one type of weather. This weather condition is deter- 
mined largely by the position and strength of the 
Bermuda high, a large semipermanent high-pressure 
area covering much of the Atlantic from 10 to 30 
degrees north latitude. The northeast trades blow 
around and out of the high’s southern rim. With a 
few exceptions during the period of the experiment, 
the wind direction at xAntigua was east-northeast. 
Once, for a period of 3 days, it went around to north- 
northeast and on two separate occasions blew from 
the east. Average daily surface wind speed was 16 
knots, with occasional variations between 8 and 27 
knots. Eepresentative air temperatures varied between 
74 and 78 F, relative humidities between 60 and 80 
per cent. The sea water temperature was reasonably 
constant at 77.5 F, with occasional variations between 
76.5 and 78. No significant horizontal gradients of 
sea temperature were found. Precipitation was Avholly 


1 

1 

-aoiaJ 


\ 

MIXED - 

“T' 

1 X 


\ 1 

MEAN SOUNDINGS 

9,10 MARCH 

■DAY 0700-1900 0-0 — 

WIND 

SURFACE ENE 17 KNOTS 
100 FT ENE 23 KNOTS 





A 


1 

1 








Y 1 

1 

1 


NIGHT 1900-0700 V-V 
WIND 

SURFACE ENE 18 KNOTS 
too FT ENE 23 KNOTS 



7 

7 

9 


\ 

4 


1 1 

1 ' 
1 


1 


WA' 

1 SUR 

Lj 

FER 

FAC 

L 


WATER 

.SURFACI 

L. J 

1 

LL 


WATER SURFACE 

L_ 1 U 


74 7 6 70 14 16 18 20 

TEMPERATURE IN DEGREES F MIXING RATIO , G/KG 


Figure 7. Mean temperature and mixing ratio curves, 
March 9 to 10, 1945. 


in the form of showers with a maximum frequency of 
occurrence around sunrise. Periods of relatively dry 
weather followed by periods of relatively showery 
weather and accompanying transitions were experi- 
enced. It is felt that these variations were caused by 
fluctuations in the intensity and position of the Ber- 
muda high or by the trough effects ahead of dis- 
sipating cold fronts. 

During the entire period of observations, a simjfie 
surface duct was found to exist over the water. From 
the second week in February through the third week 
in March, and again in the first week of April, duct 
conditions were essentially constant. This condition, 
which is called herein the normal condition, is shown 
in five figures. 

Figure 7 shows the average temperature and mixing 
ratio values for a 2-day period plotted against height. 
Curves of daytime and nighttime conditions are 
shown. Soundings were taken every 2 hours. The 


water surface values are derived from measurements 
made on the ship. Considerable difficulty was found 
in obtaining accurate soundings in the daytime due 
to radiation from the warm land in the case of the 
tower soundings and the warm ship in the case of 
ship soundings. As mentioned in Section 4.1, sound- 
ings were possible on the ship only when running with 

100 

80 

60 

*- 

UJ 

UJ 

ll. 

? 40 

X 

0 

UJ 

1 20 


340 350 360 370 380 390 40c 

MODIFIED INDEX *- 

Figure 8. Mean modified index curves, March 9 to 10. 



MIXED > 

— r 



1 1 

MEAN SOUNDINGS 

9,10 MARCH 

DAY 0700 - 1900 0-0 — 

WIND 

SURFACE ENE 17 KNOTS 
100 FT ENE 23 KNOTS 

NIGHT 1900- 0700 V-7 
WIND 

SURFACE ENE 18 KNOTS 



If 




< n 

_mL 




1 

Ji 



ivv r 1 

Lnc £ 

o r\niv lo" 



1 ^ 
1 

1 WAl 

ER SURF 
1 1 

ACE T 

L-IJ 



the wind. Thus, radiation effects of the ship were 
maximized, especially in the daytime. However, valu- 
able psychrometer measurements were made on the 
outbound runs which showed the air to be consistently 
cooler than the water. On this basis, absolute values 


100 


80 


UJ 60 


40 


20 




MlXfeoJ 

1 


1 1 

MEAN SOUNDING 

24,25 MARCH 



1 

1 

1 


WIND 

SURFACE ENE 8 KNOTS 
100 FT ENE 10 KNOTS 



1 

1 

1 







1 

I 

; 






1 

L 

WATER 

SURFACE- 

1 



340 


390 400 


350 360 370 380 

MODIFIED INDEX ► 

Figure 9. Mean sounding during low winds, March 
24 to 25. 


of temperature in the daytime tower soundings have 
been arbitrarily adjusted. 

Figure 8 is the M curve computed from the tem- 
perature and mixing ratio curves just given. The sur- 
face duct and the small diurnal change in its proper- 
ties are readily seen. An interesting point is the exist- 
ence of a rather sharp discontinuity at the 1-ft level. 


PROPAGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


41 


Careful independent measurements were made using 
a number of locations and techniques. All these tests 
confirmed the failure of the sea surface values to fit 
to the smooth curve. It appeared possible that propa- 
gation results might be more dependent on the M 
deficit as computed using the 1-ft value than on that 
computed from the sea temperature. The terms ‘‘'effec- 
tive surface values’^ of temperature, mixing ratio, and 
M were therefore established, these being defined as 
the values of these quantities at 1 ft above the water 
surface. Correspondingly, the effective value of M 
deficit is the difference between the value of M at 1 ft 
above the sea surface and the lowest value of M for a 
given sounding, and this effective value should not be 



MODIFIED INDEX ^ 


Figure 10. Mean sounding during high winds, April 
10, 11, 12, 13. 

confused with the total M deficit, which may be con- 
siderably different. This concept will be employed 
later in the paper. 

Another significant feature of the normal sounding 
is the fact that, although the minimum value of M 
is at a height of about 40 ft, the curve does not quite 
reach the slope corresponding to mixed air in the first 
100 ft. Due to the roughness of the few higher sound- 
ings obtained, it has been impossible to determine the 
exact height at which the air becomes mixed. It appears 
to be between 100 and 200 ft. 

The next four soundings show what happened to the 
duct under abnormal synoptic conditions. The major 
variations were (a) relatively low winds, (b) rela- 
tively high winds, (c) relatively dry air, and (d) rela- 
tively moist air. 

The figures which follow are mean or representative 
sample soundings made during each of the conditions 
described above. All were made on the tower and are 
chosen as best illustrating the effect on the M curve. 


Figure 9 is a mean curve for low winds. It shows a 
lowering of the top of the duct and a change in slope 
of that portion of the curve lying between 1 ft and 
the top of the duct. No marked change is found in the 
total M deficit. 

With wind speeds greater than normal, the duct 
thickness increased, the effective M deficit decreased. 



330 340 . 350 360 370 380 390 400 

MODIFIED INDEX ► 


Figure 11. Mean soundings during an influx of dry 
air, March 27, 28, 29. 


and the total M deficit also decreased slightly. The 
average of 4 days’ soundings during a windy period 
is shown in Figure 10. 

At one time there was an influx of exceptionally 
dry air with winds of normal speed. Figure 11 shows 
the effect on the M curve. The major change is an in- 
crease in the total M deficit. 

Figure 12 is a sample sounding made during a pe- 
riod when the air was relatively moist. The significant 
deviation from the normal soundings is the decrease in 


SAMPLE SOUNDING 

II APRIL 1900 

wind: 

1 

1 

1 

1 

> 




100 FEE 

II 

GENE 2! 

r KNOlb 
5 KNOTS 

1 

1 c 









0 





MIXED- 

^1 

1 

1 


o 






1 

1 

1 

1 

L 



w! 

SUf 

1 

ftTER 

'“C\ 

b 


330 340 350 360 370 380 390 400 

MODIFIED INDEX ► 

Figure 12. Mean soundings during an influx of moist 
air, March 27, 28, 29. 


the total M deficit and the lack of any change in the 
effective M deficit or in the duct height. 

In addition to the shore soundings made at the 
water’s edge, a few soundings were obtained inland, 
in an effort to determine how far in over the land the 
duct extended. Unfortunately, most of the data are 


42 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 


sparse and not too reliable. A few good soundings 
were obtained about 1 mile inland, an example of 
which is shown in Figure 13. The data were taken dur- 
ing the day and show clearly that no low duct existed 
at that time. This slide is a composite between a 
sounding made on a 50-ft windmill and a kite sound- 
ing made nearby. The kite was flown to 600 ft and the 
M curve continued at the slope representing mixed air 
from 60 ft on up to 600 ft. No night measurements 
were made. 

It was possible to make a few shipboard soundings 
to leeward of the island, beginning at a distance of 2^2 
miles and continuing on out to 20 miles. A preliminary 
study of the results shows no appreciable change over 
the course and no difference between conditions to lee- 


INLANO SOUNDING 
2 MILES FROM TOWER 
26.27 MARCH 1500-1700 



76 78 80 

TEMPERATURE 
IN DEGREES F 


82 84 


wind: 

surface: ene 8-12 knots 
100 feet: ene 11-I6 knots 


1 

1 



I* 



r 

1 


1 < 

1 

1 

1 



1 

1 

1 





1 

j 

v 



12 13 14 

MIXING RATIO 
IN G/KG 


340 360 380 
MODIFIED 
INDEX 


Figure 13. Inland soundings, March 26 to 27. 


ward and to windward of the island, indicating that 
the duct is restored very close to shore. 

Some plots of certain correlations between wind 
speed, duct thickness and M deflcit follow. The graphs 
in many cases are composed of very few points and 
due to the short time available are based on average 
soundings which have necessarily been smoothed. 
Figures 14, 15, 16, and 17 are based on the mean tower 
soundings and mean winds for each run, these being the 
only smooth data readily available for quick analysis. 

Figure 14 shows effective M deflcit plotted against 
wind speed. This portion of the curve seems sensitive 
to wind speed variation. 

Figure 15 shows the effective slope (height of min- 
imum M divided by effective M deflcit) plotted against 
wind speed. Some connection between the two quan- 
tities is indicated. 

In Figure 16 the height at which M is a minimum 
is plotted against wind speed. The isopleths of effective 
M deflcit have been sketched in. A few of the points 


were thrown out in drawing the isopleths. For constant 
duct height, the effective M deficit apparently first in- 
creases with increasing wind speed and then decreases. 
Unfortunately there are only two points in the low 
wind region to establish this behavior. It is quite pos- 



0 5 10 15 20 25 30 

SURFACE WIND SPEED IN KNOTS 


Figure 14. M deficit versus wind speed. 

sible that the lines should be more nearly horizontal 
at low wind speeds and then should slope off in the 
manner shown for winds above 15 knots. 

An attempt to plot sea temperature minus air tem- 
perature against wind speed showed no correlation. 



0 5 10 15 20 25 30 

SURFACE WIND SPEED IN KNOTS 

Figure 15. Effective M-curve slope versus wind speed. 

Plotting mixing ratio based on saturation at sea tem- 
perature minus mixing ratio computed from dry and 
wet bulb temperatures against wind speed also failed 
to show any correlation. 


PROPAGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


43 


Figure 17 is a plot of total M deficit versus wind 
speed, with isopleths of total slope, that is, the duct 
height divided by the total M deficit. Again, the exact 
pattern of the isopleths is not definitely determined. 
With the inclusion of more data in the form of 
smoothed individual soundings, this chart and the 
previous ones may prove to be more conclusive. If this 
is the case, it may then be possible to estimate the 
values of duct height and effective M deficit simply 
from single observations of air temperature, air hu- 
midity, sea temperature, and wind. Psychrometric 
observations taken at a height of from 30 to 60 ft 
above the water would provide the value of M at the 
top of the duct to ±1 or 2 H units at the most. An 
observation of sea temperature leads directly to the sea 
surface value of M, and the wind speed can be obtained 
from the ship^s anemometer. Thus with the aid of the 
charts three important points on the M curve can be 



0 5 10 15 20 25 


SURFACE WIND SPEED IN KNOTS 

Figure 16. Height of M deficit versus wind speed. 

obtained, namely, the values of M at the sea surface 
and at 1 ft and the minimum value of M and its 
height. 

These preliminary results may be summarized as 
follows : 

1. A surface duct between 40 and 50 ft high with 
a slightly transitional-type layer extending above the 
duct to between 100 and 150 ft exists most of the 
time over the water in this area. 


2. The duct is destroyed over land in the daytime 
within about ^/2 mile of the shore. 

3. Islands comparable in size to Antigua have little 
effect on the duct on the leeward side at a distance 
greater than 2^ miles off shore. 

4. The higher the wind speed the thicker the duct 
becomes and the less the ejfective M deficit becomes. 



0 5 10 15 20 25 

SURFACE WIND SPEED IN KNOTS 

Figure 17. Total M deficit versus wind speed. 

5. Changes in wind speed have little effect on the 
total M deficit, which is determined essentially by 
the temperature and humidity of the air mass as a 
whole in relation to the surface water temperature. 

6. These conditions probably prevail over ocean 
areas having comparable climates. 

4.1.3 Preliminary Results of Radio and 
Radar Measurements® 

The main purpose of the experiment was to estab- 
lish what operational use could be made of low-lying 
ducts and to confirm observation of the effects of such 
ducts on radio and radar propagation made in various 
parts of the world. The data accumulated have been 
available for study only 2 weeks, and there has been 
insufficient time for a complete analysis. As a con- 
sequence only the highlights of the agreement between 
experiment and theory have been determined. 

Ducts were present all the time, and trapping on 
both X and S bands, which increased the signals to 
levels considerably above standard propagation values, 
was found to exist all the time. The general conclusion 


®By M. Katzin, U. S. Naval Research Laboratory. 


RECEIVED SIGNAL-DB BELOW 1 WATT RECEIVED SIGNAL - DB BELOW 1 WATT 


44 


TRANSMISSION EXPERIMENTS AT ANTIGUA, WEST INDIES 




Figure 18. Composite S-band run field strengths, 
March 15. 


Figure 19. Composite X-band run field strengths, 
March 15. 



20 


30 


40 

CO 

lii 

? 50 

o 

UJ 

o 

60 


70 


80 

5 10 15 20 25 30 35 40 4 5 50 




RADAI 

R ECHO 

STRENG 
)-l5A R/ 
APRIL IS 

TH VS 1 

RANGE 






II 

J45 





m. 


\ 









L \ 











X \ 

\ 

\\ 

A 


\ 


ANT HT DIAM 

6 FT 48 II 

6 FT 29 11 

14 FT 29 II 

54 FT 39 II 

94 FT 29 II 

6 FT 29 II 

. 1 1 

DISH 

N. 

M. 

^ 


!:p 





N.- 

N. 

N. 1 

1 1 

» APR 




'•o 



RANGE NAUTICAL MILES 


Figure 20. Composite X-band run field strengths, 
April 10 to 11. 


Figure 21. Radar echo strength versus range for 
various antenna heights. 


PROPAGATION IN S AND X BANDS IN LOW-LEVEL OCEAN DUCTS 


45 


regarding the effect on the two bands was that on S 
band antennas as high as the experiment would allow 
gave the highest signal strengths. On X band, on 
the other hand, the lowest antenna heights which were 
available usually gave the strongest signals. 

Figure 18 is an S-band run made on March 15. It is 
a composite run containing the results of both the 
outward and the inward runs. Several of the curves 
have been omitted for clarity. The highest curve is 
for a combination of a 46-ft transmitting antenna 
and 94-ft receiving antenna. The lowest curve is for 
the two lowest heights, 16 and 14 ft. The slopes of the 
curves are rather steep for the first 80 miles or so, 
the signal declining considerably less rapidly there- 
after. Also, the variation of the signal with height is 
shown here to be in the order in the extremes between 
25 and 30 db. This interval from 80 to 50 db shows a 
difference between the two extremes of 30 db. To trans- 
late that into a radar situation, double that difference 
to get a difference of 60 db, showing that on S band 
the higher antenna combinations would provide con- 
siderably better coverage for targets in the order of 
100 ft high and with transmitters at the height of about 
50 ft. Stated another way, the highest antenna com- 
bination would provide coverage beyond that obtain- 
able with the lowest in the order of 30 miles. 

There is as yet no reasonable explanation for the 
extremely slow decrease in signal beyond 80 miles. 
This feature is very distinctive in the S-band curves. 
For the X band, it is generally not discernible except 
on a few runs toward the extreme range portion. The 
rate of decrease of signal with range in the region 
inside 80 miles would be exponential if there were a 
straight line on this figure. Considering it to be so, 
averaging over a number of runs gives roughly 0.8 db 
per nautical mile. That decrease is the total amount, 
the 1/R variation not having been extracted from it. 
Attempts to do so show that the resulting curve does 
not, in a plot of this sort, fit a straight line as well 
as the original values themselves, but if the 1/R value 
is taken out of the power relation the average attenua- 
tion is then roughly between 0.5 and 0.6 db per nau- 
tical mile. In this region (beyond 80 miles), on the 
other hand, the decrease of signal with range is con- 
siderably less, being between 0.15 and 0.2 db per nau- 
tical mile. No satisfactory explanation for this be- 
havior has yet been derived. 

Figure 19 shows the X-band results for the same 
period. Antenna heights of 16-ft transmitting and 


6-ft receiving produced the highest curve, the lowest 
curve being obtained on a 46-ft to 94-ft combination. 
Note that succeedingly higher antenna combinations 
produced successively lower signal strengths. There is 
some variation, but when the curves are smoothed 
to a straight line the attenuation is on the order of 

0.33 to 0.5 db per nautical mile. Eemoving 1/R re- 
duces the attenuation to roughly 0.2 db per nautical 
mile. There is no sharp bend in the curve at about 80 
miles, as was the case on the S band. The lowest (16- 
ft to 6-ft) antenna combination showed more than 
35 db greater signal strength than the highest (46-ft 
to 94-ft) combination. Considering again the radar 
case, it is found that the higher antenna provides rela- 
tively poor coverage compared to the lower. In terms 
of range for a given signal threshold, the difference in 
favor of the lower antenna is about 80 miles. 

Figure 20 shows an X-band curve obtained during 
April 10 and 11, when a transmitting antenna height 
of 8 ft was available. Eeceived signal powers for 6-, 
14-, 24-, 54-, and 94-ft receiving antennas are shown. 
The curves are somewhat scrambled, but the general 
result is that the lowest antenna again produces the 
greatest signal, with increasing antenna height pro- 
ducing progressively smaller signals. This was not the 
case without exception, as can be seen in Figure 4, 
where the 6- and 14-ft antennas exhibit comparable 
behavior. In that case the maximum range was ob- 
tained on the 14-ft antenna. The average slope in 
Figure 20 is somewhat less than that shown in Fig- 
ure 19. Exact averages of all the runs have not yet 
been worked up. 

Figure 21 shows a plot of received signal versus 
range, made on a 3-cm radar, using a PC boat as a 
target. The highest curve was obtained with a 6-ft 
antenna height, using a 48-in. dish to obtain greater 
gain and range. The other run with 6-ft antenna was 
made using the regular 29-in. dish. There is a consider- 
able spread in the values of received signal due to the 
difficulty of measurement. However, the significant 
thing is that the maximum ranges obtained are in 
accord with the indications given by the one-way trans- 
mission results. Striking an average slope shows the 
decrease of signal with range to be about 1.0 db for 
each 1.5 nautical miles. 

The important conclusions can be summarized as 
follows : 

1. The surface duct is very persistent. 

2. The duct is very effective in extending the ranges 


46 


TRANSMISSION EXPERIMENTS AT ANTIGUA, VEST INDIES 


obtainable on both S and X bands, for either one-way 
or two-way transmission. 

3. On S band, the highest combination of trans- 
mitting and receiving antennas produces the strong- 
est signal and the greatest range. 

4. On X band, the lowest combination of transmit- 
ting and receiving antennas produces the strongest 


signal and the greatest range. 

5. Surface ducts in the trade wind reginiia ean be 
used for communication purposes to a eoikserratiie 
range of 100 miles. Greater ranges are piobabie bot 
will require further investigation. 

6. Rain in the form of squalls does not apprectablj 
affect the received signaL 


Chapter 5 

TRANSMISSION EXPERIMENTS IN ENGLAND 


5 1 BRITISH TRANSMISSION 

EXPERIMENTS^^ 

Introduction 

T he beoad object of the studies carried out in 
Great Britain during the past few years has been 
to establish the characteristic facts of the propagation 
of centimeter waves (more recently of meter waves 
also) and especially to determine the relationship be- 
tween radio performance and meteorological condi- 
tions in the lower atmosphere, with forecasting as the 
ultimate aim. 

Although propagation of 10-cm waves to distances 
much beyond the optical range had been observed 
under favorable conditions nearly a decade earlier, 
it was the striking increases in range of decimeter 
and centimeter wave coastal radars in southern Eng- 
land, observed in the summers of 1940 and 1941 re- 
spectively, which led to a concentrated attack on the 
long-range aspects of the problem. About the same 
time a need arose for more accurate knowledge of both 
the short-range “interference” field and the long- 
range “diffraction” field for certain communication 
projects, and the radio equipment developed to meet 
this need formed a nucleus round which the later and 
more ambitious experiments grew. 

The various experimental and theoretical aspects 
of this work were reviewed in some detail at the meet- 
ing of the Ultra Short Wave Propagation Panel under 
whose auspices the work is being done, in London 
on October 6, 1944 ; these reviews have been circulated 
as listed in references 1 through 15. 

Continuous observations have been carried out over 
a range of optical and nonoptical paths across the Irish 
Sea on S and X bands and over a single 38-mile land 
path on S band. These are discussed below. In addi- 
tion to this work several investigations of more specific 
propagation problems have been carried out during 
the summer of 1944. 

1. Measurements on two wavelengths in S band, 
over a 70-mile sea path between a site in South Wales 
and the summit of Snowdon (3,500 ft). This optical 
path was studied to obtain data on the probability 

*By E. C. S. Megaw, Ultra Short Wave Panel, Ministry of 
Supply, England. 


of missing aircraft on S-band radars under conditions 
favorable to trapping at low levels over sea. 

2. Measurements on a wavelength of about 3^/2 m 
over a 90-mile sea path, with heights such that the 
path length was about twice optical range, to provide 
quantitative data on the importance of refraction in 
this waveband. 

3. Radar measurements from Llandudno, North 
Wales, with the Isle of Man and the Irish Coast as 
the main targets, on S, X, and K bands. The object 
was to obtain practical data on the relative perform- 
ance of K band under a variety of meteorological 
conditions which were studied simultaneously with 
the radar observations by ship, balloon, and aircraft 
measurements. Some further reference to the results 
of (1) and (2) appears below; an interim report on 
(3) has been circulated.^^ 

Irish Sea Measurements 

The first plant for simultaneous measurements 
within and much beyond the optical range on wave- 
lengths of about 9, 6, and 3 cm, using heights of 
about 100 and 500 ft each site, was made in the 
latter part of 1941. 

The work was planned on an inter-service basis, 
with equipment provided by Admiralty (developed 
under Admiralty contract by General Electric Com- 
pany Research Laboratories from that used in the 
early communication studies mentioned above) and 
stations provided and operated by Signals Research 
and Development Establishment, Ministry of Supply. 
Arrangements were made for analysis of the data by 
the National Physical Laboratory, which has also 
more recently undertaken the development of moni- 
toring equipment. The collaboration of the Meteoro- 
logical Office was received at an early date, but it 
was only when the study of the subject had made 
further progress that the need for detailed low-level 
meteorological measurements was realized; these have 
been undertaken by the Naval Meteorological Service, 
soundings being made in ships and by means of ship- 
borne balloons. Additional arrangements have recent- 
ly been made with the Meteorological Office for regu- 
lar aircraft soundings over the path. 


47 


48 


TRANSMISSION EXPERIMENTS IN ENGLAND 


Some difficulties were encountered early in 1942 
in finding sites for the stations which were accept- 
able from all points of view, and the field work done 
in that year consisted of several short-period trials 
over a rather wide variety of land and sea paths. In 
spite of many limitations, in particular as regards 
detailed meteorological data, the general conclusions 
reached in these trials® have been largely substan- 
tiated by later measurements. Table 1 gives details of 
the sites finally adopted. 


Table 1 


Station 

Height, ft 

S. Wales (transmitters) 

A. Garn-Fawr 

540 

B. Strumble Head 

90 

N. Wales (receivers) 

C. Rhiw 

825 

D. Aberdaron 

95 

Scotland (receivers) 

E. Knockharnahan 

375 

F. Portpatrick 

95 


The path length from South Wales (A and B) to 
North Wales (C and D) is 57 statute miles and that 
to Scotland (E and F) is 200 statute miles. The path 
lengths in terms of geometrical optical range for the 
eight possible paths are shown in Table 2. 


Table 

2. Transmission path 

lengths. 

Path 

AC BC AD BD 

AE AF BE BF 

Distance in units 



of optical range 

0.89 1.21 1.40 2.40 

3.82 4.92 5.63 8.45 

Distance (miles) 

57 

200 


In the original scheme all the paths were to be 
collinear, but this could not be realized with the 
sites finally adopted; the South Wales to Scotland 
paths differ by about 17° in bearing from the South 
Wales to North Wales paths, the bearing of the 
former being within a fraction of a degree of true 
north. A scheme for recording data over all paths 
(though necessarily not continuously) was evolved; 
each transmitter l)eam was aimed for half the time 
along each of the two bearings 17° apart (a 7y2- 
minute period was found the most satisfactory, and 
a small change in frequency (5 to 10 me) was made 
automatically when the beams switched over. 

At each frequency the transmitted signal consisted 
of square pulses, at equal on/off ratio, with a repeti- 
tion frequency of 1000 c. The ^^standaiMT’ power out- 
put in the ^^on^’ period was 0.6, 0.3, and 0.15 w for 9, 
G, and 3 cm, respectively; the signal records were 


corrected for any significant departure from these 
powers. Paraboloid mirrors 48 in. in diameter were 
used for all transmitters and receivers; these were 
mounted inside the stations behind large canvas- 
covered ^Vindows.’’ The increase in mirror gain with 
frequency more than made up for the reduction in 
transmitter power, in spite of the less effective utiliza- 
tion of the mirror area. In the receivers the 1,000-c 
component of the modulation was rectified to operate 
the recording milliammeters. Provision had been made 
for monitoring the field radiated from the trans- 
mitters and the sensitivity of the receivers, in terms 
of a standard radiated field. This scheme was brought 
into operation as the National Physical Laboratory 
equipment became available ; other less complete 
methods of monitoring the transmitters and check- 
ing the receivers had been in operation from the start. 
(Data for the 5-cm equipment are included here 
although, as will be noted, it was not used.) 

Radiotelephone communication between the North 
Wales and South Wales stations has been maintained 
satisfactorily for two periods of several months each 
using first S- and later X-band equipment, essen- 
tially the same as that used for the signal measure- 
ments, arranged for duplex operation. A meter-wave 
system (which gives more continuous service over 
long nonoptical paths) is now being installed by Ad- 
miralty Signal Establishment to link all the stations; 
it is already operating satisfactorily over the 57-mile 
path, and a relay link from North Wales to Scotland 
is being provided. 

On S band, operation on all four links across the 
57-niile path commenced in November 1943, although 
the two from Station A (high site) had been running 
since July. During the preliminary period, up to the 
beginning of 1944, in which a number of practical 
difficulties had to be overcome, the radio results were 
subject to rather more uncertainty than was the case 
in the earlier measurements where a concentration of 
experienced personnel was possible for the short peri- 
ods involved, and detailed analysis of these results has 
not yet been attempted. One S-band receiver was in 
operation in Scotland (Station F, low site, 200 miles) 
from the end of August 1943, but apart from one 
brief period during September, no signals were re- 
ceived until March 1944, just before the second S- 
band receiver (Station E, high site) was installed. 

On X band all the stations were in operation by 
July 1944, operation on the 200-mile links having 
started a month earlier. 


BRITISH TRANSMISSION EXPERIMENTS 


49 


Alter rt few iiioiitlis of operation of all 1(5 links it 
was realized that the available elTort would not be 
sufficient to cope adequately with the tasks of editing 
and examining the signal records. Consequently a 
rather drastic reduction of the centimeter wave pro- 
gram was agreed to for a trial period of 6 months, 
starting October 1, 1944. For this period the follow- 
ing links were operated continuously (without beam 
switching) : on S band, A to C and D (57 miles) and 
B to E (200 miles) ; on X band, A to C and B to D 
(both 57 miles). (The possibility of a link from B 
to D on S band with separate equipment was also 
envisaged.) 

It was agreed to postpone operation on 6 cm, but 
at least one 3 V 2-111 link over each of the two path 
lengths would be added; preliminary measuiements 
on this longer Avavelength were already being made. 
In addition, K-band equipment for at least the optical 
57-mile path was to be installed at an early date. 

Figure 1 shows a general view of the equipment in 
one of the stations ( D ) . The X- and S-band receivers 


are in the center of the picture, with tlic mirrors and 
canvas-covered windows behind. The S-band signal 
generator and monitoring equipment are on the small 
table beside the S-band receiver. The recorders are 
mounted on a temporary table (now leplaced by the 
central control desk), extieme right. The empty bay, 
extreme left, was designed to house the K-band equip- 
ment. The meter-wave equipment was mounted in an 
adjoining room. 

In addition to the radio measurements, some study 
was made of the behavior of a light beam over the 
57-mile path during the summer of 1944 in the hope 
that this might provide useful information on the 
refraction produced (nearly) by temperature gradient 
alone. Measirrable changes in elevation were some- 
times observed by means of a theodolite, but the in- 
cidence of adequate visibility was small, and little 
quantitative information was obtained. 

A detailed study of the S-band signal records and 
meteorological data obtained from February 1944 is 
being made at the National Physical Laboratory, par- 



Figure 1. General view of the equipment in Aberdaron, North Wales. 




50 


TRANSMISSION EXPERIMENTS IN ENGLAND 


ticiilarly for the 57-niile paths AD and BD.^ Similar 
study of the S band and 3y2-meter data will follow. 

Figure 2 shows a plot of hourly mean signal level 
for the S-band signal over the links AD and BD for 
June 1944, with a record of some meteorological fac- 
tors — fronts, precipitation, and fog — with which com- 
parison has been made. 


7. While periods of high level are sometimes char- 
acterized by large gradients of water vapor (sound- 
ings usually made for the first 200 ft, at one point near 
the center of the path), no satisfactory correlation 
has been found between the character of the M curve 
and the major variations in signal level for the peri- 
ods which have been studied. In general, as is com- 



Figure 2. Signal strength in decibels above 1 nv receiver input, June 1944, drawn from hourly mean values. 


It should be emphasized that analysis of the data 
obtained during this period has not yet been com- 
pleted, but the following general conclusions may be 
drawn : 

1. There is general agreement between signal vari- 
ations for the two paths, though the short-period 
variations often differ. 

2. Signals are obtained over the 200-mile path 
only when signals over 57-mile path BD exceed about 
30 db above 1 fx\. But if the latter condition is ful- 
filled the former does not always follow. 

3. There is a marked diurnal variation, when the 
general level is low or moderate, with high signal in 
the late afternoon or evejiing and low level in the 
early morning. 

4. There is evidence for an appreciable seasonal 
variation with high level for a greater fraction of the 
time in summer than in winter or spring. 

5. Low level occurs commoidy in conditions of 
fog or low visibility (e.g., low level on 174 occasions 
out of 233 on which fog was recorded between Feb- 
ruary and June 1944). 

6. Low level is usually observed at the passage of 
fronts (e.g., on 78 occasions out of 106 on which 
fronts were recorded). 


mon experience for similar paths, high levels tend to 
occur in anticyclonic periods. 

The general character of the S-band signal varia- 
tions for the four 57-mile paths is illustrated by the 
plots of hourly mean levels for 5 days in August 1944 
shown in Figure 3. The range of variation in level 
increases with the excess of path length over optical 
range, and there is an obvious similarity between the 
three nonoptical paths as regards the larger changes 
in level. This similarity does not extend to the optical 
path AC^, which shows signs of an inverse correlation 
with the major variations of the nono})tical paths. 
F"or a standard atmosphere (% earth radius) the 
receiver on the AC. ])ath is near the record maximum 
of the interference field. For fairly small departures 
from standard (curvature corresponding to, say, 1.0 
to 1.7 times earth radius) the range of variation 
caused l)y interference is quite small, about -|-4 to 
— 7 db relative to free space field; the smallness of 
the variation is due to the appreciable effect of diverg- 
ence of the rellected ray in this case. 

While other factors beside interference with the 
rellected ray are almost certainly operative in produc- 
ing variations over the oi)tical path, slow fading with 
a range of the order of 10 db is quite common; and 


BRITISH TRANSMISSION EXPERIMENTS 


51 








: ""L ''■■■■ 



V 


A,-*C, LINK 

20 > ^ 






rs 







\ A 

TV 


STp. 

Si 





V 

w 

^ V 


LINK 







Figure 3. Signal strength in decibels above 1 nv receiver input. FS: Free space signal. STD: Standard signal. 
SL: Sensitivity limit. 


a slightly substandard index gradient, which would 
produce a marked decrease in level for the nonoptical 
paths, would leave the AC path in the neighborhood 
of the first interference maximum. 

The free space levels (48 db above 1 /xv from A, 
44 db from B; difference due to different radiated 
powers at this period; IV 2 db estimated atmosjiheric 
absorption allowed for) are marked on the plots of 
Figure 3. For all four paths the highest levels reached 
are in the neighborhood of the free space value ; levels 
several decibels above free space are occasionally 
reached during good periods, but they are only rarely 
maintained for as much as a few hours (e.g., path 
BD, May 12, 13 and August 5, 6). The long-time 
average level for path AC should be close to free space 
level, probably about 2 db above. It is actually about 
5 db below for the first half of August 1944 and 
about 3 db below over a period of several months. 


While some of this discrepancy may be due to residual 
experimental error, the fact that it appears to be 
least during periods of poor transmission between the 
low stations (e.g., August 10 in Figure 3) may be 
significant. 

For the nonoptical paths BC, AD, and BD the 
standard level is 20, 37, and 79 db below free space 
level, respectively, for S band. The corresponding 
figures for X band are 28, 53, and 113 db. The stand- 
ard level is shown in Figure 2, and in Figure 3 for 
paths BC and AD ; for path BD it is over 30 db below 
the receiver threshold. While it is rare, during the 
summer months, for the level to remain near stand- 
ard for a large fraction of the time (in February, 
however, the AD level was within 2 db of standard 
for about 25 per cent of the time), the minima of 
the major signal variations usually lie within about 
±5 db of the standard level except (1) during runs 


52 


TRANSMISSION EXPERIMENTS IN ENGLAND 


of ])aitic'iilarly <^oo(l weathc'r and (2) during ioggy 
conditions which arc likely to l)c associated witli a 
substandard index gradient. Striking examples of the 
latter occurred on June 4, 5 (Figure 2) and August 
10, 11 (Figure 3). Ou the last occasion the BC level 
went about 20 db below standard. 

The X-band results for the 57-inile paths are gen- 
erally similar to those for S band as regards the major 
variations, but the range of variation is noticeably 
larger, particularly on paths BC and AD, which are 
not much longer than optical range; the increase in 
range of variation for these paths is of the same order 
as the ditference in standard level for the two wave- 
lengths. In general, short-period variations are larger 
and more rapid for the shorter wavelength. 

Figure 4 shows the results for both S and X l)ands 
over the 200-mile paths AE (high stations) and BF 
(low stations) for part of the same period as shown 
in Figure 3. After allowing for the estimated atmos- 
pheric absorption (6 db for S, 16 db for X) the free 
space levels are similar for the two wavelengths, ex- 
perimental uncertainty being appreciably greater at 
X band as regards absolute values. The standard 
levels are, of course, far below the receiver threshold, 
actually about 275 db for path AE on S and 400 dh 
for path BF on X. 


A . 

0 

l\ • 

— TREE SPACE 

j\/ 


1 

9ATH A— E 

A 1 

1 V 

• 

1 

1 

S BAND 

A 

%o 

J 



1 




r40 

08 

30 

20 

10 

0 


30 


^rRCC SPACE 


•• 

•• 

1 

A 


i 

j 

> 

i 

o 

A / 


1 


V 


IV 


PATH A— E j 

1 

A' 


1 





!\ 

X BAND 1 

, 


20 

10 


SIGNAL STRENGTH IN DB ABOVE IaV RECEIVER INPUT 


i 'W* 

r^ A m * / 


-•rfttE iPACE 




PATH B^r 

y 

• 

1 

\ 

S BAND 


30 

20 

10 

0 


• 

li 



— TREE SPACE 


i 



j 

e 1 

1 

0 


o* 

1 


PATH B -*r 


I 


. J 



X BAND 


40 

30 

20 

10 

O 


Auc e 


AOC 7 


AUG 8 194 4 


Figure 4. Hourly mean values of signal strength on 
S and X band. 


'The most striking characteristic of the results is 
})erhaps the similarity in magnitude of the signals 
both for the two paths and for the two wavelengths. 
In general, signals are measurable for a greater frac- 
tion of the time on the longer wavelength and for 
the higher sites. (The ditference of about 5 db in re- 
ceiver threshold sensitivity between S and X has only 
a slight effect on this.) At the peak of good periods 
the lower sites and shorter wavelengths sometimes 
reach rather higher levels, as in the case of the 57- 
mile paths the maximum signal level is frequently 
comparable with free space; rather rarely it exceeds 
free space level by something of the order of 10 dh. 
For the 200-mile path the possible error in the esti- 
mate of atmospheric absorption is rather more serious, 
particularly for X band, but it seems improbable that 
this could alter the general character of the results. 

Comparison with the results for the 57-mile BI) 
path in the bottom record of Figure 3 is interesting 
and is reasonably typical of the extent to which the 
performance of the long path can be predicted from 
the performance of the shorter one. It should be em- 
phasized that this Avas a period of good summer 
Aveather apart from the break on August 10-11. 

5.1.3 Overland Measurements: Whitwell 
Hatch to Wembley 

A single S-band liidv has been in continuous ojiera- 
tion over this 38-mi Ic path since iMarch 1043. Its 
terminals, Avith the transmitter in one of the Ad- 
miralty Signal Establishment buildings and the re- 
ceiver at General Electric Company Research Labora- 
tories, AA^ere chosen for operating convenience rather 
than to meet any si)ecial requirements for the path, 
as an important subsidiary purpose Avas to ])rovide for 
controlled long-period tests on equipment developed 
for use in the less readily accessible stations of the 
Irish Sea program. Apart from routine checks the 
equipment normally operates unattended; automatic 
frequency control at the receiver has been in operation 
since June 1943. But the receiver is provided Avith a 
relay-operated alarm Avhich can be set to operate on an 
abnoianal change of received level in either direction 
(normally doAviiAvards) and this has proved valuable 
in calling attention to both faults and nnnsual propa- 
gation conditions. 

The transmitter is on a hill 725 ft above sea level 
and the path runs nortliAvards across the Thames 
valley and the Avestern outskirts of London to the 
receiver, Avhich is oidy 170 ft above sea level, in low, 


BRITISH TRANSMISSION EXPERIMENTS 


53 


uiicliilatiiig, built-up country. For standard conditions 
the path is clear except for the last mile where trees 
and houses form a barrier elevated about degree 
above the ray path. This introduces a local diffraction 
loss at the receiver which has been estimated roughly 
at about 30 db. This estimate is necessarily an un- 
certain one, both because of the complexity of the 
real barrier (which is approximated as one or more 
opaque straight edges) and because of possible sea- 
sonal variations. 

Seasonal variations in general signal level have been 
observed with a maximum in late summer of the order 
of 10 to 15 db higher than the single winter minimum 
recorded so far. An attempt to explain this variation 
in terms of changes in the horizontal plane diffraction 
pattern of part of the barrier with varying opacity of 
the tree background does not appear to be supported 
by tfie results of the past few months (Summer 1944) . 
The mean level for the whole period is, however, close 
to 30 db below free space (52 db above 1 julv receiver 
input) and is thus at least of the same order of mag- 
nitude as the estimated standard level. The unfor- 
tunate effect of this uncertainty regarding standard 
level is mitigated to a considerable extent by the fact 
that a land path of this kind gives an easily definable 
^^eneraF’ level, which is in fact that obtained under 
^Svell-mixed’^ meteorological conditions. 

Further details of the path and a discussion of the 
results in relation to general meteorological conditions 
over the path have been given in two National Physical 
Laboratory reports, which cover the first year’s 
operation. A further report is in preparation. The aim 
here is limited to a general description of the type 
of results obtained, with examples of some character- 
istic signal records. 

Figure 5 gives a plot of hourly mean level for March 
1944 which clearly shows the two main characteristics 
of the signal : the reasonably constant general level 
and the regular diurnal cycle which occurs with radia- 
tion nights. The period March 21 to 26 is typical of 
an undisturbed run of clear nights; note the period 
of marked substandard signal in the early morning of 
March 27, indicating that condensation near the 
ground has reduced the water vapor content there suffi- 
ciently to make the lapse rate negative. Intermittent 
rain in bad weather periods usually gives a more vari- 
able level than cloudy weather with no precipitation; 
a small rise in level is often observed with continuous 
rain (direct effects of rain on the equipment have been 
carefully guarded against and may be assumed negli- 



WHITWCLL hatch WCMBLCY path, march 1944, S-BANO 
HOURLY mean INTENSITIES IN DB ABOVE l/rV RECEIVER INPUT 

Figure 5. Whitwell Hatch to Wembley path, March 
1944. S-band hourly mean intensities in decibels above 
1 /xv receiver input. 

gible) and a more marked rise with clear skies in 
daylight following rain. These effects are readily ex- 
plicable in terms of changes in water vapor distribu- 
tion. 

The work of the past 6 months (Summer 1944) has 
shown a definite correlation of high level at night with 
temperature inversion whether with clear or with 
variable skies; on the other hand, clear or variable 
skies with no temperature inversion (e.g., with incom- 
ing cold air) show no night peak of signal. In general 
the increase of level on an initially clear night is 
arrested by the development of low cloud or of fog. 
Double maxima are often observed in the night peaks 
(e.g., March 15 in Figure 5). 

The magnitude of the peaks on radiation nights is 
usually 5 to 10 db; it can occasionally reach 15 to 
20 db particularly in summer. It seems very probable 
from the geometry of the path that earth-reflected rays 
play little part, at least for moderate degrees of bend- 
ing. It is therefore reasonable to seek to explain the 
larger variations as resulting from increasing ray 
curvature. In terms of the rough estimate mentioned 
above, a change from standard to “flat earth” condi- 
tions would give an increase in level of the order of 
10 db, which is a typical figure for the observed rise 
on an undisturbed radiation night. It is of interest to 
note that free space level is never reached on this 
path; the highest instantaneous level reached is 10 to 
12 db below free space. In other words complete, or 
nearly complete, reflection regions do not exist at 
heights of the order of 1,000 ft or more (required to 
“clear” the barrier) over this path. This is in line with 
the observed lack of any effect of high inversion on the 
signal level. 


54 


TRANSMISSION EXPERIMENTS IN ENGLAND 


Figures 6, 7 , and 8 show photographs of sections 
of the original signal records illustrating the main 
types of signal which are observed. The type of weather 
involved is shown on the record in each case, also the 
signal calibration. Figure 9 shows a good example of 
an effect which is quite often observed, particularly 


200 ft per hour and 300 ft per hour respectively. No 
local soundings are available to check this hypothesis, 
but the calculated rates of change of height are quite 
possible. 

The general meteorological data for the night (illus- 
trated in Figure 9) are as follows: cloudless, follow- 


TIME IN HOURS GMT 



j ' CjLdMpT **1, H 

- PI r"p t * ‘ 




Figure 6. Signal records. (A) June 4, 1944 from midnight till noon. Weather cloudy, light W wind, intermittent rain. 
(B) June 11, 1944, 6 a.m. to 6 p.m. Weather clear in the morning, later cloudy; light W wind, intermittent rain. 


in the latter part of radiation nights. It consists in a 
regular variation showing the characteristic rounded 
maxima and sharp minima of interference fading. This 
is in some cases superimposed on a nearly steady high 
signal (as in Figure 9). In other cases, as in some fog 
fades, it is superimposed on variations of a different 
type. It often starts and stops suddenly, completely 
changing the character of the record while it lasts, and 
that time ranges from one or two fading cycles to many 
cycles. This sort of effect has also been observed on 
other paths, over sea as well as land. 

The striking thing about patterns of this sort is that 
they often correspond to reflection coefficients for the 
interfering ray which approach unity. In Figure 9 
the reflection coefficient calculated from the pattern 
is about 0.8 at the start, about 0.4 in the middle, and 
over 0.9 at the end. It is suggested that reflection at 
small glancing angles from a sharp inversion top pro- 
vides a possible explanation and that the first part 
of the pattern in Figure 9 corresponds to an increase 
in height (the first deep minimum occurring when 
the inversion top is just above the transmitter) and 
the latter part to a decrease in height at a different 
rate. The rates of climb and fall turn out to be about 


ing a fine day ; temperature inversion of about 6 F in 
(approximately) the first 500 ft at 0600 GMT ; ground 
mist about dawn. It is clearly desirable to obtain ade- 
quate soundings at periods when this type of effect is 
observed, especially on account of the widely held view 
that the index changes which occur at heights of the 
order involved (about 500 ft above ground level) are 
inadequate to account for reflection coefficients of the 
size implied by the pattern observed here. 

5.1.4 Difficulties of Existing Theory 

In this section a few general characteristics of the 
radio observations which appear to be at variance with 
previous theoretical conclusions and which suggest 
directions in which further work is required will be 
noted. 

1. The most obvious point as far as the Irish Sea 
data are concerned is the failure of the soundings to 
provide an adequate guide to the signal variations. The 
fault may lie in the limited nature of the soundings or 
in the method of interpreting them, but it is clear that 
the problem is by no means as simple as was supposed 
when the soundings were started. 

2. The minimum levels obtained (where they are 


TIME IN HOURS GMT 


HRITISH TRANSMISSION EXPERIMENTS 


o 


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000 O o 

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55 


gnal records. (C) June 20 to 21, 1944, Strong NE winds, little cloudy, (D) August 28. Cloudy in the early morning changing into contin- 
n clearing with freshening SW wind. (E) Shows passage of a warm front on May 4, 1944, at 5:30 p.m. followed by a cold front 1 hr later. 



56 


TRANSMISSION EXPERIMENTS IN ENGLAND 


liigli enough to be measured) usually agree tolerably 
well with the expected values. For the Irish Sea paths, 
as well as in other measurements, the maximum level 
rarely goes above that calculated for flat-earth condi- 
tions; this level is practically the same as that for 
free space conditions for all the Irish Sea centimeter 
links except for paths BF on S band (only) where 
there is a difference of about 10 db. If complete guid- 
ing were a common phenomenon over paths of the 
lengths actually used, it would appear that levels above 
free space should occur much oftener and more con- 
tinuously than is observed. It appears to be a useful 
working assumption that the level obtained under 
favorable conditions over nonoptical paths is nearly 
that calculated for rays with the same curvature as 
the earth. 

3. The fact that the Irish Sea results show that (for 
centimeter waves) the advantage lies only rarely with 
the smaller heights and shorter wavelengths suggests 
that the importance of complete guiding as a criterion 
for siting stations may have been overemphasized. 

4. The good correlation obtained in a number of 
cases between land-sea temperature difference and 
signal level suggests that the importance of tempera- 
ture may be greater than is indicated by existing 
theory. 

5. It appears very difficult to account for the max- 
imum levels reached on the basis of existing theory. 

6. The interference patterns of the type discussed 
above in Section 5.1.3 still await an adequate explana- 
tion. 

5 2 PROPAGATION WORK IN PROGRESS 
AT THE NATIONAL PHYSICAL 
LABORATORY^ 

This report gives a summary of the present position 
(November 1944) of various investigations being con- 
ducted under the auspices of the Ultra Short Wave 
Propagation Panel of the R.D.F. Applications Com- 
mittee of the Advisory Council on Scientific Research 
and Technical Development, Ministry of Supply. The 
items to which the Radio Division of the National 
Physical Laboratory is contributing may be listed 
as follows : 

1. Analysis and study of centimeter and meter 
wave propagation over sea (3-6-9) experiments. 

2. Study of properties of water vapor, water, and 
ice, and the absorption and scattering by these and 
other substances in the atmosphere. 


3. Measurement of reflection coefficient of land at 
centimeter wavelengths. 

4. Study of centimeter wave propagation over land 
(Whitwell Hatch to Wembley). 

The following sections indicate the progress that 
has been made to date on items 1 and 4. For items 2 
and 3, see Sections 10.5 and 9.3. 

Analysis and Study of Centimeter 

and Meter Wave Propagation over Sea 
(Irish Sea Experiment) 

This project utilizes the results of radio transmis- 
sions being conducted between two sending stations 
in South Wales and receiving stations in North Wales 
and Scotland, jointly by the Admiralty, Ministry of 
Supply and Air Ministry. 

The contribution of the National Physical Labo- 
ratory to the installations being used for this investiga- 
tion has been chiefly connected with the monitoring 
equipment used at both sending and receiving stations 
to insure that the radiation from the former and the 
sensitivity of the latter are maintained constant, so 
that any variations on the field strength records are 
known to be due to transmission effects in the atmos- 
phere. The instruments required for the S band are in 
an advanced state of production, while for the X band 
the necessary field strength meter for the transmitters 
has been developed, but some development work is 
still required on the standard radiator for the receiver 
calibration. In accordance with a recent agreement as 
to the limitation of the scope of the investigation, all 
work on instruments for other wavelength bands has 
been put in abeyance. 

^ Study of Centimeter Wave 
Propagation over Land (Whitwell 
Hatch to Wembley) 

A transmitter operating on a wavelength in the S 
band has been installed at the Admiralty Signal Es- 
tablishment, Whitwell Hatch, and a continuous record- 
ing is being made of the field intensity of the radiation 
received at the Research Laboratories of the General 
Electric Company, Wembley, over a land path of 38 
miles. Except for some houses and trees within about 
5 miles of the receiver, the path is a clear optical one; 
originally the transmitter was also partially obscured 
by some trees, removal of the tops of which produced 
a rise in received field of 10 db. Field strength re- 
cording has been in progress over this link since 


‘’By W. Ross, British Central Scientific Office. 


TIME IN HOURS GMT 


PROPAGATION WORK AT NATIONAL PHYSICAL LABORATORY 


57 



(H) January 15, 1944, typical for widespread, thick fog. 


58 


TRANSMISSION EXPERIMENTS IN ENGLAND 



Figure 9. Signal record. August 26 to 27, 1944, showing examples of interference fading in radiation nights. 


March 1943, and during the intervening 18 months 
there has been a seasonal variation, with the average 
daily value in November and December at least 10 db 
below the value in July and August. Two reports^®’^^ 
have already been issued on the results obtained from 
an analysis of the records, and a third will be pre- 
pared shortly. 

Among the main conclusions so far reached are the 
following. Cloudy weather, either by day or night, 
tends to produce a signal steady to within about 2 db, 
while on days of clear and variable skies, the signal 
exhibits slow (period 5 to 10 minutes) fluctuations of 
the order of 3 or 4 db, with sharper and more rapid 
fluctuations superposed. These rapid fluctuations are 
accentuated by the presence of strong wind. On nights 
of clear or variable skies with temperature inversions 
near the ground, the fleld intensity is from 5 to 10 
db above the daytime level and is usually accompanied 
by variations in the absence of wind. On clear radia- 
tion nights, when the wind is too strong to permit the 
development of a temperature inversion, the peak of 
signal intensity does not occur. Fog affects the fleld 
strength differently according to its depth. A shallow 
autumn fog causes a sharp decrease in signal strength, 
while the widespread and more established type of fog 
experienced in winter may sometimes cause marked 
interference type of fading with unusually high peak 
values and at other times may have no apparent effect 
on the fleld strength. 

The sending and receiving stations on this link are 
now being equipped with fleld strength monitoring 
arrangements to improve the overall accuracy of the 
radio recording, and a daily statement of the meteoro- 
logical conditions over the path is being supplied to 
supplement the ground station records already avail- 
able. It is contemplated that this link should remain 
in operation for a further period of 6 to 12 months. 


5 3 FADING IN A LINE-OF-SIGHT 
EXPERIMENT IN ENGLAND‘S 

This experiment was carried out between Aberporth, 
South Wales, and the summit of Mt. Snowdon (3,600 
ft). The transmitters were mounted at a height of 
120 ft above sea level at Aberporth, the receivers being 
on Mt. Snowdon. The length of path was about 60 
miles as compared with 85 miles optical range. 

Two separate radio circuits were used, one on a 
wavelength of 9 cm and the other on 10 cm. For a 
standard atmosphere the phase difference between the 
ray reflected from the sea and the direct ray was about 
4.5 radians on 10 cm and about 5 radians on 9 cm, 
while under ‘^flat earth” conditions the corresponding 
phase differences were about 12 radians and 13 radians 
respectively. As the atmospheric conditions varied, an 
interference pattern was obtained arising from varia- 
tions in the phase difference. The chief characteristic 
of the interference pattern was that in a plot of radio 
signal strength against time the peaks are broad and 
flat and the minima are sharp and deep. The provision 
of the two circuits insured that the variations du^e to 
alterations in the phase difference could easily be 
distinguished from variations due to other causes 
(described below). The reason for this is that the 
interference minima on one circuit tend to occur at 
times when the signal strength is high on the other 
circuit. 

The length of time required for the radio signal 
strength to complete a cycle of the interference pat- 
tern was usually about 2 hours. The receivers and 
transmitters were very carefully calibrated in order 
to show that the received field strength at interference 
maximum was equal to twice the free space field. This 

®By F. Hoyle, Ultra Short Wave Panel, Ministry of Supply, 
England. 



TEMPERATURE EFFECTS ON NONSTANDARD RANGES 


59 


result was established to within an accuracy of zb 2 db. 

For about 20 per cent of the time (June 1, 1944 to 
September 30, 1944) the normal interference pattern 
Was replaced by an entirely different form of signal 
fading. The period of the fading was about 5 minutes, 
the field strength at maximum was usually between 
10 and 12 db above the free space signal, and the 
peaks of signal were sharp and the minima broad. The 
latter characteristic is entirely different from interfer- 
ence fading between two rays which must lead to 
broad peaks and narrow minima; it is more akin to 
receiver noise or the form of the signal echo received 
from ^Vindow” on radar sets. Thus it would seem 
plausible to suppose that the signal was the result of 
a large number of contributions with uncorrelated 
phases. 

The type of fading described in the previous para- 
graph is especially interesting in view of the very high 
signal maxima. It was shown that the occurrence of 
these variations was not associated with the reflection 
at the surface of the sea. It would appear therefore 
that atmospheric conditions can exercise a very im- 
portant effect on the propagation of radio waves over 
a completely optical path. 

5 4 TEMPERATURE EFFECTS ON 
NONSTANDARD RANGES'^ 

Experimental work carried out in the Irish Sea has 
shown the following three characteristics, all of which 
are in disagreement with existing theory. 

1. It is well known that the present theory requires 
the contribution of the temperature gradient to be in 
general small compared with the contribution of the 
water vapor gradient. In fact if we write 

d& , dT / “I \ 

'dh~°''Sh dh’ ^ 

where /x = refractive index, 

e = partial pressure of water vapor, 

T = temperature in degrees absolute, 
h = height coordinate, 
a, h are positive constants, 

then except in rare cases the present theory requires 
the (a) (de/dh) term to be large compared with the 

^By F. Hoyle, Ultra Short Wave Panel, Ministry of Sup- 
ply, England. 


(h) (dT/dh) term. Thus, since the radio propagation 
conditions depend on dfi/dh, it is to be expected that 
a better correlation will exist between the radio signal 
and the measured value of {a) {de/dh) than between 
the radio signal strength and the measured value of 
( — b) (dT/dh). The reverse has, however, been found 
to be the case ; the correlation between the radio signal 
strength and the measured value of (a) (de/dh) is 
poor, while the correlation with the measured value of 
( — &) (dT/dh) is good. 

2. A situation similar to that mentioned in (1) has 
been encountered in attempting to forecast 12 hours 
ahead for operational radar sets. Table 1 summarizes 
the results obtained. 


Table 1 


Forecasting 

No. of cases 

% of correct 

system 

examined 

forecasts 

(de/dh) term 

600 

56 

Continuity method 

600 

57 

(dT/dh) term 

150 

75 


The continuity method of forecasting consists in pre- 
dicting that tomorrow’s conditions will be the same as 
those observed today. Forecasting from the (dT/dh) 
term was empirical, it being assumed that a tempera- 
ture inversion of 1.5 C per 100 ft would give very good 
propagation conditions, an inversion of 0.75 C per 
100 ft would give good conditions, and a temperature 
lapse would correspond to standard or natural condi- 
tions. 

3. The value of d^/dh calculated from equation (1) 
using the measured values of de/dh and dT/dh are too 
small to explain the large signals frequently observed 
on a wavelength of about 80 me. 

These experimental results enable the following 
conclusions to be drawn so far as the meteorological 
conditions around the British Isles are concerned. 

1. The radio signal strengths computed from the 
observed M curve do not agree with observation. The 
method of observing the temperature and water vapor 
gradients to obtain an M curve is therefore unsatisfac- 
tory. 

2. A reasonably satisfactory forecasting system can 
be obtained on the basis of temperature gradient alone. 
This system is empirical and does not depend on com- 
plicated mathematical computations. Accordingly the 


60 


TRANSMISSION EXPERIMENTS IN ENGLAND 


system may be suitable for application under opera- 
tional conditions.® 

®It has appeared since the November 1944 Propagation 
Conference that the Propagation Group at San Diego has 
found a good correlation between the radio data and a simple 
meteorological parameter based on temperature excess. In the 
British Isles the temperature excess has to be taken between 


a height of about 200 ft and sea level, whereas at San Diego 
the temperature excess has to be taken between a height of 
about 5,000 ft and sea level. It has also been reported that in 
the Pacific Area temperature excess is by far the best index 
for predicting radio propagation conditions. There is some 
hope, therefore, that it may be possible to work out a method 
of fairly universal application on the basis of temperature 
excess. 


PART II 


METEOROLOGY 




Chapter 6 

METEOR(^LOGY— THEORY^ 


1 MODIFICATION OF WARM AIR BY 
A COLD WATER SURFACE^ 

History 

T wo OF THE COMMONEST TYPES of M curves which 
produce nonstandard propagation are the S-shaped 
curve and the simple trapping curve where M decreases 
from the surface to 200 ft, say. The S-shaped curve 
occurs in regions of subsidence, for example, in the 
extensive subtropical anticyclones. The forecasting 
of this phenomenon will not be presented in this dis- 
cussion which is confined to the simple trapping case. 

During 1943 the question arose regarding the 
feasibility of forecasting the change in the temperature 
and vapor pressure distribution as warm air flows over 
a cold water surface. Through practice, considerable 
success had already been obtained in forecasting the 
M curve a few miles offshore in Boston Harbor. How- 
ever, it was suggested that a general method be de- 
vised whereby the M curve could be predicted for 
greater distances from the shoreline and for different 
regions of the world. In order to solve this forecast 
problem the Boston Harbor soundings were investi- 
gated in the light of turbulence theory. 

Two factors had to be kept in mind, namely : 

1. The Boston Harbor soundings of temperature 
and vapor pressure were scant. A more serious diffi- 
culty was the total absence of data at distances in 
excess of 15 miles from the land. 

2. Since forecasting techniques were the primary 
aim it was necessary to find a solution which was 
suitable for field use. 

Diffusion Equation 

The differential equation for turbulent mass ex- 
change may be written 

0 ) 

dt dz\ dz/ 

[f K, the coefficient of eddy diffusion, is assumed con- 
stant, then 



“See also Parts H and HI of Chapter 17, Volume 1, Com- 
mittee on Propagation. 

‘’By J. M. Austin, Meteorology Department, MIT. 


where E = error function, that is, 

\Tr Jo 

T' = temperature at a level z over the ocean, 
T = initial temperature at z over the land, 
Tq = initial air temperature over land at 2 : = 0, 
Ty, = water temperature, 
t = time. 

Values of K were then computed from the observa- 
tional data by evaluating the ratio (T' — T)/{Tq — 
for different evaluations and different times. These 
values were averaged for each level and the results 
shown in Table 1 were obtained. After plotting K 


Table 1. Values of K. 


Eleva- 






tion 






in ft 

20 

50 

100 

200 

300 

K 

0.014X104 

0.07X104 

0.18X104 

0.38X104 

0.67X104 


against elevation, the approximate linear variation 
of K was extrapolated to give values of K for eleva- 
tions up to 700 ft. This level of 700 ft lies well within 
the limit of 250 m which was indicated by Mildner^ 
to be the^ level where K reaches its maximum. 

These values of K were then used to construct Table 
2, which gives (T' — T)/{Tq — Ty,) for all levels in 
terms of the time that the air has been over the water. 
The same values of K were obtained from the analysis 
of vapor pressure changes; hence the same table can 
be used to evaluate the ratio (e' — e)/(eo — From 
this table it is a simple matter to reconstruct the M 
curve at any distance over the ocean, provided the 
initial state of the air is known. An example of the 
changes in the M curve are given in Figure 1. 

® Discussion of Procedure 

Summarizing the favorable aspects of this study, 
it can be stated that: 

1. The values of K were almost identical for vapor 
pressure and temperature changes. This suggests that 
the data were reliable. 

2. The values of K agreed with those of GibletP 
for wind variations from the surface to 150 ft. 

3. This extrapolation method, that is, the error 
function extrapolation, gives reasonable values after 


63 


64 METEOROLOGY— THEORY 



Table 2. Values of (T' 

- T)/iTo 

- Ty,) 

or (e' — 

e)/(eo - 

By,); initially To > Ty,, eo < By,. 



Elevation 
in ft 

H 

14 

H 

1 

IVz 

Time in hours 
2 3 

4 

6 

10 

15 

20 

0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

' 1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

20 

0.23 

0.40 

0.49 

0.55 

0.63 

0.67 

0.73 

0.77 

0.81 

0.85 

0.88 

0.89 

50 

0.17 

0.34 

0.43 

0.50 

0.58 

0.63 

0.69 

0.73 

0.78 

0.83 

0.86 

0.88 

100 

0.09 

0.23 

0.33 

0.40 

0.49 

0.55 

0.63 

0.67 

0.73 

0.79 

0.83 

0.85 

150 

0.04 

0.15 

0.24 

0.31 

0.41 

0.48 

0.56 

0.61 

0.67 

0.74 

0.80 

0.82 

200 

0.02 

0.10 

0.19 

0.25 

0.35 

0.42 

0.51 

0.57 

0.64 

0.71 

0.77 

0.80 

250 

0.01 

0.08 

0.15 

0.22 

0.31 

0.38 

0.47 

0.54 

0.62 

0.69 

0.75 

0.78 

300 

0.01 

0.07 

0.14 

0.20 

0.29 

0.36 

0.45 

0.52 

0.60 

0.68 

0.74 

0.77 

350 

0.01 

0.05 

0.11 

0.17 

0.26 

0.33 

0.43 

0.49 

0.58 

0.67 

0.73 

0.76 

400 

0.00 

0.04 

0.09 

0.14 

0.23 

0.30 

0.40 

0.46 

0.55 

0.65 

0.70 

0.74 

450 

0.00 

0.03 

0.07 

0.12 

0.20 

0.27 

0.37 

0.43 

0.53 

0.63 

0.68 

0.72 

500 

0.00 

0.03 

0.05 

0.10 

0.17 

0.24 

0.34 

0.40 

0.51 

0.61 

0.67 

0.71 

550 

0.00 

0.02 

0.04 

0.08 

0.15 

0.22 

0.32 

0.38 

0.49 

0.59 

0.65 

0.70 

600 

0.00 

0.01 

0.03 

0.07 

0.13 

0.20 

0.29 

0.35 

0.46 

0.57 

0.64 

0.69 

650 

0.00 

0.01 

0.02 

0.06 

0.11 

0.18 

0.27 

0.33 

0.44 

0.55 

0.62 

0.67 

700 

0.00 

0.00 

0.01 

0.05 

0.10 

0.16 

0.25 

0.31 

0.42 

0.53 

0.61 

0.66 


All values are negative. 


a long period of time. A check was made by compar- 
ing Taylor’s data off Newfoundland with computed 
values. This check was quite good. 

4. The procedure is simple, and consequently the 
weather officer could readily calculate the M curve. 

However, the entire method may be criticized be- 
cause : 

1. In the integration of the diffusion equation K is 
assumed constant while in the application of the in- 


to -32c Eo- 12.3 MILLIBAR 
T^-22 C E^- 26.5 MILLIBAR 



Figure 1. Changes in M curves resulting from modifica- 
tion of warm, dry air over cool, moist surface. Zero time 
corresponds to the coast line; 34 hr, 4^ hr, etc,, refer 
to the time the air has been over water. 

tegrated formula K was found to vary with elevation. 
The values of K which were used in the final analysis 
are therefore ‘^effective values.” 

2. K has been considered to be independent of the 
degree of roughness (probably a justifiable assumption 
over the ocean), the degree of stability, and the wind 
velocity. These factors were neglected solely because 
the scant data did not allow a complete analysis of 
the variation of K. 


These ‘^effective values” should give some indication 
of the true variation of K. They suggest that K varies 
linearly with elevation except for a quite rapid increase 
in about the first 30 ft. Consequently it seems reason- 
able to assume that 



li K = pz q then, from the statement that 
K {hu/hz) = constant (eddy stress does not vary with 
height), the velocity variation with elevation is given 

I'y 

= a log (2 + 6) + C. 

4die question now arises: In the laminar layer, is the 
wind variation with height represented by a logarith- 
mic law? 

6.1.4 Previous Investigations 

For many years research workers have studied the 
wind variation near the ground. A few of the conclu- 
sions will now be presented. 

1. In 1932, Sutton^ assumed a certain form of the 
coefficient of correlation between the velocities of the 
air particles considered at time t and at an interval 
of time later. This assumption implied that there 
was a power law for the variation of wind with height. 

u / z\^ n 



2. In 1933, Cardington and Giblett^ analyzed an 
extensive series of observations at 4 ft and 143 ft. Of 
course with only two points the observations could be 
made to fit either a power law or a logarithmic law. 
If a power law held, then m is a function of the degree 


DIFFICULTIES OF LOW-LEVEL DIFFUSION PROBLEMS 


65 


of stability and wind velocity. If a logarithmic law 
held, then K is a function of these same quantities. 

3. In 1934, Best^ analyzed data which was meas- 
ured at seven elevations between 2 cm and 5 m. He 
concluded that the velocity variation was best repre- 
sented by a logarithmic function of the form 

u — log {z — C) 
where (7 is a constant. 

Furthermore he found that the power law could be 
applied only to shallow layers and even then m varies 
quite considerably with height, wind velocity, and 
vertical temperature gradient. 

4. In 1936, Sutton,® who in 1932 suggested the 
power law variation, definitely favored the logarithmic 
variation. Furthermore he showed how one could 
handle the problem of varying stability. Sutton an- 
alyzed different sets of data, ranging to 30 m in 
elevation, to support the logarithmic variation. 

5. In 1936, Sverdrup® criticized Sutton’s logarith- 
mic law and favored a power law in regions of stability. 
As evidence he introduced Eossby and Montgomery’s’’ 
analysis as well as his own data. 

6. In 1937, Sutton® quite satisfactorily met Sver- 
drup’s criticism and pointed out that all experimental 
evidence suggested the logarithmic variation rather 
than the power law variation. 

This represents only a cross section of opinion and 
perhaps may be summarized as follows: 

1. In an indifferent or unstable atmosphere the 
logarithmic law is generally accepted. 

2. In a stable atmosphere there is more support 
for the logarithmic law than for the power law. 

One writer summarized the situation very aptly 
when he said that all modern mathematical studies 
on atmospheric turbulence are inexact and depend 
on certain wide assumptions. An appeal to experiment 
is therefore essential. 

Conclusion 

The question now arises, should one assume a 
power law variation, or is the true wind variation 
better represented by a logarithmic law? Certainly 
the experimental evidence tends to favor a logarithmic 
variation. The advantages and disadvantages of either 
assumption may be summarized briefly as follows: 

1. Power law variation. 

a. 7n varies with stability, wind velocity, rough- 
ness, and elevation. 

b. The mathematical analysis is too complicated 
for practical use. 


2. Logarithmic law variation. 

a. Agrees reasonably well with experimental 
data. 

b. Agrees with von Karman’s logarithmic law. 
von Karman has shown that this law covers 
an exceedingly wide range of turbulence. 

c. K, like w, varies with stability, wind velocity, 
roughness, and elevation. 

d. If the logarithmic law holds, K is then a 
linear function of height. With this relatively 
simple expression for K it should be much 
easier to handle the diffusion equation than 
in the case of a power law variation. 

e. Provided the integration of the diffusion equa- 
tion is not too complicated, one should be able 
to reconstruct the temperature and vapor 
pressure curves. Consequently the exact shape 
of the M curve can be calculated. 

In conclusion it should be borne in mind that 
theoretical discussion is futile. At best we can only 
make certain assumptions and derive a result. If this 
result agrees with observational data then the original 
assumptions are justified. Furthermore, practical con- 
siderations demand that the final solution be simple 
enough for application in the field. 

It seems certain that over a wide range of elevation, 
say 300 ft, the true wind variation cannot be uniquely 
defined by one specific logarithmic law or one specific 
power law. The most desirable procedure may then 
be an analysis of observations in as simple a manner 
as possible but yet flexible enough to take care of the 
most important changes. Consequently it is suggested 
that experimental data be analyzed on the assumption 
that K varies linearly with elevation, i.e., 

dT d ( dT\ dT d / dT\ 

dt dz\ dzj dx dz\ dzj 

where K = pz q, and x is the distance measured 
horizontally. If accuracy is not seriously affected it 
is further suggested that approximations be intro- 
duced in order to facilitate the application of the 
results for field use. 

62 DIFFICULTIES OF LOW-LEVEL 
DIFFUSION PROBLEMS^ 

The effect of a temperature inversion is largely a 
secondary one in that by reducing the coefficient of 
diffusion it favors the formation of large humidity 

®By Lt. Comdr. F. L. Westwater, Naval Meteorological 
Service, Royal Navy. 


66 


METEOROLOGY— THEORY 


gradients. The coefficient of dili'iision K is calculated 
from the wind profile which is assumed to satisfy a 
power law of the form U = Az^. 

The difficulty arises because m is fixed once and 
for all before we solve the equation and thus the 
theory cannot take account of changes in the tempera- 
ture gradients of a diurnal character in so far as they 
affect the humidity distribution. At the same time we 
believe that K is very sensitive to the temperature 
gradient. 

Further, values of m have been used which have no 
meteorological support. The value m = 0.5, for ex- 
ample, implies a wind structure which is absurd if 
extended up to 100 m and it certainly is invalid near 
the ground. Chemical warfare technique measures m 
directly by measuring R, the ratio of the wind at 2 m 
to the wind at 1 ni. Even in the very extreme condi- 
tions which prevail over land no value of K exceeding 
1.35 is observed. This makes m = 0.33. Over the sea, 
even in a low layer, it is very unlikely that a value of 
m differing significantly from Yj would be found. 

The difficulty is that power laws apply only for very 
limited ranges of height and can be extended only by 
using a different power. Their only merit is that they 
enable the equation of diffusion to be solved; the 
power law is not a law of nature. A complete solution 
of the problem would involve a theory giving K as 
a function of temperature gradient. A start has been 
made on this for the case of still air which is agitated 
by thermal turbulence originating from heating on 
its lowest level. The value of K so calculated is small 
compared with that for a light wind. It seems likely 
that the effect of an inversion on K will also be small. 

To sum up, radar personnel should be warned that 
the diffusion theory is at present in a highly unsatis- 
factory state ; any conclusions drawn from it should be 
treated with the greatest reserve, and some calcula- 
tions already published are based on assumptions 
which have no meteorological foundations. 

6 3 PRELIMINARY RESULTS OF METEOR- 
OLOGICAL MEASUREMENTS IN 
MASSACHUSETTS BAY*^ 

The modification produced in land air when it 
passes out over water is known to be particularly effec- 
tive in producing nonstandard microwave propaga- 
tion. The preliminary results of this study are covered 
in the present report ; they are necessarily incomplete 
and tentative. 

‘*By R. B. Montgomery, Radiation Laboratory, MIT. 


6.3.1 Modification of Air Flowing 
over Water 

To begin with, some basic considerations will be 
presented. Figure 2 shows an airplane sounding in air 
which is warm and dry relative to the underlying 
water. Before leaving land the air was vertically 
homogeneous ; that is, potential temperature and 
specific humidity were constant. This may be seen 
by comparing the observed temperature and vapor 
pressure with the broken straight lines drawn for 

OCTOBER 19. 1944 1141-1203 C-231 

5 MILES north of PROVINCETOWN. MASS q ASCENT 

SURFACE WIND WEST 4 0 . SECOND ASCENT 



TEMPERATURE VAPOR PRESSURE M-M,, 

IN DEGREES C IN MILLIBARS 

Figure 2. Typical airplane sounding, giving temper- 
ature and water vapor variation with height, 

homogeneous air. The straight line of modified index 
of refraction M is constructed for homogeneous air; 
it is close to standard. The air is being modified by 
loss of heat to the water and by evaporation. 

At the common boundary the temperatures of air 
and water are identical. The vapor pressure also is 
given by the water temperature; over sea water the 
vapor pressure is 98 per cent of the saturation value 
corresponding to the water temperature. It follows 
that the modified index at the surface is determined 
by the water temperature alone. 

Figure 2 illustrates in a striking manner the simi- 
larity in shape of the three curves. The ratio of the 
change from unmodified value at any height to the 
change at the surface is the same for all three quan- 
tities. 

Modification of air over w'ater is due largely to 
turbulent mixing, which transports heat and water 
vapor in exactly the same manner (the eddy dif- 
fusivity is identical for both). Next to the water 
boundary there is always a laminar layer, through 
which heat is transported to the turbulent layer by 
true conduction while the water vapor is transported 
by true diffusion ; the coefficients for these two related 
processes happen to be nearly the same, so heat and 
water vapor are transported vertically to nearly the 



PRELIMINARY RESULTS OF METEOROLOGICAL MEASUREMENTS 


67 


same relative degree. The temperature distribution is 
modified by radiation also, but for an initial period 
of a few hours this is unimportant compared with the 
processes just mentioned. 

When initially homogeneous air flows over water of 
constant temperature, a necessary result is therefore 
that the curves of temperature and water vapor pres- 
sure are similar. Furthermore the M curve is similar 
also, because within the range of any sounding the 
modified index is approximately a linear function of 
temperature, vapor pressure, and height. 

The extent of similarity revealed in Figure 2 is 
unusual. Often the three curves have very different 
shapes. In the latter case the deviation from simi- 
larity can be ascribed (1) to lack of homogeneity in 
the unmodified air, (2) to varying water temperature 
along the aiFs trajectory, or (3) to radiation during 
prolonged over-water modification. 

The M Deficit 

The distances on the base line from the straight 
broken line to the arrow are the temperature excess 
and humidity deficit respectively. There is obviously 
a corresponding quantity pertaining to index of re- 
fraction. The M deficit may be defined as the value 
of the modified index at the water surface less the 
representative surface value in the unmodified air. 

Temperature excess, humidity deficit, and M deficit 
are related, so any two fully determine the difference 
between unmodified air and air at the water surface. 
The two of most direct significance are M deficit and 
temperature excess. Forecasting is simplified by their 
use: Temperature excess is necessary in drawing the 
temperature curve ; similarity and M deficit then give 
the M curve directly. Another advantage in using 
M deficit is that whether it is positive, zero, or nega- 
tive determines at once whether the modified air is 
probably characterized by an M inversion (layer 
where modified index of refraction decreases upward) 
by standard, or by substandard M curves, respectively. 
For instance, the positive M deficit in Figure 2 is a 
condition necessary for the M inversion to occur. 

Specifically, if homogeneous air blows over a water 
surface of constant temperature and if the M deficit 
is positive, there is always an M inversion at the 
water surface. Whether or not this extends sufficiently 
high to be of importance in the refraction of radio 
waves depends in part on the magnitude of the M 
deficit and on the temperature excess. 

If homogeneous air blows over a water surface of 


constant temperature and if the M deficit is zero, the 
M curve necessarily remains practically standard. 

In the case of a negative M deficit a substandard 
M curve is developed. It should be noted that in this 
case (as well as in the previous one) the air is losing 
water vapor by condensation on the water surface. 
This is simply the reverse of the process with dry air. 


Neutral Equilibrium 

For simplicity the analysis which follows is limited 
to cases of positive M deficit. There is then a surface 
M inversion, the height of which is a convenient 
quantity to study as a dependent variable. The inde- 
pendent ones are M deficit and temperature excess 
and, as will be seen, two others. 

The first and least complicated case is the one of 
neutral equilibrium, which corresponds to a tempera- 
ture excess close to zero, say within 1 C of zero. Since 
there is no appreciable temperature gradient, the M 
curve depends only on the moisture distribution. 
Furthermore this case practically requires a vapor- 
pressure lapse at the surface, because in the lower 
part of a homogeneous layer the vapor cannot be 
saturated (see Figure 3). Hence there is always an 
M inversion at the surface. Neutral equilibrium is 
prevalent far from shore. 



DEGREES C 



Figure 3. Probable course of modification of warm air 
over water under ideal conditions. A, initial stage. 
D, final stage. 


With neutral equilibrium frictional turbulence is 
unhindered. Mixing extends to a height roughly pro- 
portional to the wind speed; a wind of 20 mph at 
100 ft gives mixing up to about 2,000 ft. 

The intensity of mixing increases upward rapidly 
from the surface, so large vertical gradients are con- 
fined to the region of relatively little mixing close to 
the surface. The M inversion probably never extends 
above 100 ft. 


68 


METEOROLOGY— THEORY 


It lias been well established that under neutral 
equilibrium the eddy diffusivity is directly propor- 
tional to height within the so-called turbulent bound- 
ary layer, which forms the lower tenth of the entire 
frictional layer mentioned above. In this case wind 
speed, temperature, and vapor pressure are linear 
functions of the logarithm of elevation. 

While the details are not presented here, it is easily 
shown that these logarithmic distributions demand 
that the height of the top of the M inversion be 

d = |o rAM10-«, 

O 

where a is the radius of the earth, is the M deficit, 
and r is a meteorological parameter depending on 
wind speed alone in the case of complete neutral 
equilibrium. Thus the height of the M inversion is 
directly proportional to the M deficit with neutral 
equilibrium. 

Published data indicate that the effect of wind 
speed is not great and give an average value of P = 

0.08. This yields d/^.M = 2 ft. Data obtained during 
the summer’s (1944) project agree with this result. 

Unstable Equilibrium 

The second case is the one of unstable equilibrium 
or negative temperature excess. This is similar to 
neutral equilibrium in that the M deficit is always 
positive and there is always a surface M inversion. 

Instability adds convective mixing to the frictional 
mixing that would otherwise be present. This con- 
vective mixing is especially effective in the central 
region of the unstable layer and hence confines the 
large vertical gradients within a still thinner surface 
layer. 

The logarithmic distributions are characteristic of 
neutral equilibrium only. Consequently, in the un- 
stable cases the height of the M inversion is not simply 
proportional to M deficit but depends on M deficit in 
a more complicated manner. In spite of this the pro- 
portionality will be assumed as a useful approxima- 
tion in studying the unstable and stable cases also. 

The ratio of height of M inversion to M deficit is 
definitely less for unstable than for neutral equili- 
brium. Tentatively it may be said to range between 
0.2 ft and 2 ft. 

Stable Equilibrium 

The last case is the one of stable equilibrium. Sta- 
bility reduces the mixing with high levels, thus per- 
mitting a deeper surface layer of strong gradients to 


form (as shown in Figure 2). Thus the ratio of heiglit 
of M inversion to M deficit may be expected to be 
always greater in stable equilibrium than in neutral 
equilibrium. 

Stability reduces the mixing to such an extent that 
the air is progressively modified during a long over- 
water trajectory. It is therefore necessary to introduce 
a fourth independent variable, length of over-water 
trajectory, to supplement M deficit, temperature ex- 
cess, and wind speed. 

Under ideal conditions there is reason to believe 
that the modification would pursue the course sketched 
in Figure 3. The final state would be an essentially 
homogeneous layer capped by a temperature inversion 
at the level already mentioned for the top of the fric- 
tionally produced turbulence in neutral equilibrium. 
The temperature of the layer would follow an adia- 
batic lapse rate from the water surface to the top. 
The water vapor would be saturated at the top of the 
layer, specific humidity being nearly constant through- 
out the layer except for a strong lapse at the surface. 
Intermediate stages in the formation of this final state 
are indicated qualitatively in Figure 3. 

It should be noted that the later stages have a 
transitional or S-shaped M curve and that qualitative 
theoretical considerations do not reveal which. The 
initial stage is, however, characterized by simple sur- 
face trapping, and it is this stage only for which data 
are presented below. 

The soundings have been studied to determine em- 
pirically how the ratio of height of M inversion to M 
deficit depends on temperature excess, wind speed, 
and length of trajectory. To eliminate complex M 
curves the analysis has been limited to cases con- 
forming closely to the following ideal conditions. 

1. Initially homogeneous air. 

2. Constant surface-water temperature along the 
air trajectory. 

3. Constant wind (wind not changing with time 
following a parcel). 

The ratio of height of M inversion to M deficit is 
found to increase with length of over- water trajec- 
tory quite markedly in the first 10 miles. From 10 
miles to 30 miles there is not much further increase. 
Beyond 30 miles the preliminary analysis reveals no 
general information. 

Figure 4 gives some tentative results based on 
various sources of information. This includes the cases 
of neutral and unstable equilibrium in addition to 
stable equilibrium. Within the stated range of over- 


METEOROLOGY OF TRANSMISSION EXPERIMENTS 


69 



WIND SPEED AT 1000 FT IN MPH 

Figure 4. Ratio of height of M inversion to M deficit. 

For positive temperature excess the over-water trajec- 
tory is 10 to 30 miles. 

water trajectory this diagram gives the height of the 
M inversion as a function of temperature excess, wind 
speed, and M deficit. A complete analysis of the ob- 
servations will yield similar diagrams both more ac- 
curate and more detailed. These should prove of 
definite use in forecasting M curves. 

In conclusion, it should be made clear that the work 
summarized in this report is a group undertaking. 
A large number of persons, some of them members 
of Radiation Laboratory Group 42 and other mem- 
bers of the U. S. Army Air Forces, took part in the 
development and construction of the instruments and 
in the observing. 

METEOROLOGY OF THE SAN DIEGO 
TRANSMISSION EXPERIMENTS® 

During the summer of 1944 a rather intensive ex- 
perimental propagation program was carried on in 
San Diego area. The main purpose was to determine 
the distribution of radiated radio energy in the lower 
troposphere under the wide range of weather condi- 
tions prevailing during this season. A temperature 
inversion was present from around the first of June 
through October; the base of the inversion varying 
from the surface, on a few occasions, up to an alti- 
tude of some 4,000 ft. This inversion is characterized 
by dry superior air subsiding over moist maritime 
polar air. 

6.4.1 Methods of Observation 

The field strength data were taken in two ways. A 
fixed one-way link between San Pedro and San Diego 

®By Lt. A. P. Stokes, U. S. Navy Radio and Sound Laboratory. 


gave continuous records on frequencies of 52, 100, 
and 547 megacycles, and vertical airplane sections 
taken at several different distances west of San Diego 
gave almost instantaneous records of the energy dis- 
tribution for the same range of frequencies. 

The meteorological data were obtained by the use 
of an airplane and wired sonde; the technique of the 
latter was described in detail in a previous report.® 
The captive balloon or wired sonde is a modified ver- 
sion of the Washington State College equipment.^® 
Daily soundings were taken at the Scripps Pier at 
La Jolla, 11 miles north of the laboratory. Two 1-week 
periods of continuous shipboard soundings were made 
from a Y"P ship operating in the middle of the San 
Pedro to San Diego link. 

The principal use of the airplane has been in tak- 
ing vertical field strength sections seaward from the 
laboratory. During these flights meteorological sound- 
ings were made as frequently as possible. The labora- 
tory was fortunate in obtaining from the Washington 
State College group one of their original sonde units 
and has adapted this equipment for use in the air- 
plane soundings. The temperature and humidity ele- 
ments were mounted in an unobstructed aluminum 
housing approximately IV 2 ft above the nose of the 
PBY-5A airplane. 

Since the airplane served the dual purpose of ob- 
taining both meteorological and field strength meas- 
urements, all the data were obtained on a fixed course. 
Field strength sections were made in rapid descente 
and the meteorological data were obtained in ascents. 
Navigational difficulties prohibited spiraling for the 
meteorological data and therefore these soundings 
covered considerable horizontal distance. Due con- 
sideration of this was made in plotting the cross 
sections. 

6.4.2 Diego High Inversion 

In the summer season San Diego lies within the 
belt of the subtropical anticyclones, and, with the 
absence of surface frontal activity, a stagnant circula- 
tion exists. Because of the persistence of high-level 
anticyclonic circulation aloft, pronounced subsidence 
is maintained throughout this season; 1944, in par- 
ticular, was characterized by very low humidity above 
the 2-km level. By subsidence aloft a thermal inver- 
sion exists over a large maritime area and thus forms 
the boundary between the lower maritime polar and 
the continental tropical or superior air aloft. Varia- 
tion in height and magnitude of the inversion is the 


70 


METEOROLOGY— THEORY 


governing factor in daily weather plienoniena. There 10,000-ft levels. It is found that with the intensifica- 
exists a close correlation between the height of the tion of the pressure field aloft, the lapse rate of tern- 
base of the inversion, the pressure at 10,000 ft, and perature approaches the dry adiabatic condition and 
the lapse rate of temperature between the 5,000- and thus, under these conditions, indicates increased sub- 



METEOROLOGY OF TRANSMISSION EXPERIMENTS 


71 


sidence. Consequently the depth of this marine struc- 
ture is diminished by the lowering of the base of the 
inversion. 

Figure 5 shows the typical structure of a moderately 
high inversion. Usually the lapse rate of temperature 
below the base approaches, and in some cases exceeds, 
the dry adiabatic condition. This vertical mixing in- 
sures a homogeneous air mass characterized by the 
constant vapor pressure in the marine stratum. 

Figure 6 shows the typical elevated S type M curve 
for this condition. 



Figure 6. M curve corresponding to the inversion shown 
in Figure 5. 


The discontinuity surface between the two distinct 
air masses exists over a large area. Soundings have 
been confined within a 130-mile radius of the labora- 
tory, but observations on an FC radar indicate trap- 
ping conditions existing between San Diego and Guad- 
alupe Island 225 miles to the southwest. 

® Shape of the Inversion Surface 

Emphasis must be placed on the fact that the dis- 
continuity surface is not horizontal over the area but 
is at any time a warped surface. Figure 7 shows a 
series of M curves taken by airplane to the seaward 
of the laboratory. Both the height of the inversion 
and gradients in the transitional layer vary greatly 



Figure 7. M curves at different distances and times. 

with distance. Repeated soundings indicate that the 
apparent slope is not due to large scale lowering dur- 
ing the time interval between observations. The cluster 
of M values along the mean lapse rate of M in the 
upper and lower strata indicates the homogeneity of 
the two air masses along the vector. The possibility 
of the coexistence of elevated and surface gradients 
has been considered. No significant surface discon- 
tinuities have been detected. 

There is a general tendency for the base of the in- 
version along the shore to have a maximum height at 
0800 and a minimum at 1600. Through the exchange 
of meteorological data between the University of Cali- 
fornia at Los Angeles and the laboratory this fact is 
now fairly well established. 

Figure 8 is a plot of refractive index from a series 
of plane soundings. The diagonal lines show the 
height and distance from the base at which measure- 
ments were made. Each line is marked with the time 
of beginning and ending the flight. The numbers at 
the ends of the curves are the refractive index (n — 1) 
multiplied by 10®. The indices are independent of fre- 
quency for this range. Again it is noted that conditions 
vary along the vector. 

Figure 9 is a plot of refractive index taken by air- 
plane along the San Diego-San Pedro path, indicat- 


72 


METEOROLOGY— THEORY 


» 



-I 1 l~T^ ^ A . . I I I I ^ I 1 ■ 

10 20 30 40 50 60 70 80 90 II 110 120 130 

MILES 


IO*FEET 



10 FEET 



10 FEET 



IO*FEXT 




10 20 30 40 50 60 

MILES 


NAUTICAL MILES 


Figure 8. Isopleths — refractive index [(n — 1) 10®] 



COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


73 



ing the magnitude and height of the strong gradients 
along the path. The time interval of each sounding is 
shown on the appropriate section. 

Again it must be emphasized that the discontinuity 
takes the shape of a warped surface, that the gradi- 
ents vary from point to point, and that the maximum 
air density change occurs in the region of maximum 
refractive index gradient. Interface waves in the 
density discontinuity are possibly superimposed on 
the already nonuniform structure. These small inter- 
face waves are evident by the undulations on the top 
surface of the stratus cloud deck. The top surface of 
the cloud deck, which is often present, marks the air 
mass boundary and is thus a good indicator of the 
base of the inversion. 

It is therefore evident that meteorological observa- 
tions required for a thorough study of propagation 
conditions must be as extensive as possible. 


6 5 TABLES FOR COMPUTING THE 
MODIFIED INDEX OF REFRACTION, 

Introduction 

The index of refraction of the atmosphere, modi- 
fied for use on a plane-earth diagram, is a quantity of 
great importance in the study of radio wave propaga- 

^By E. R. Wicher, Columbia University Wave Propagation 
Group. 


tion. It is defined by 



where n = ordinary index of refraction, 

h = height above sea level (not ground level), 
a = radius of the earth. 


The equation for n is obtained from Debye’s theory 
of the dielectric constant of gases. In terms of atmos- 
pheric quantities, equation (1) assumes the form 


Ap De Be 

M = ^-Y+Y^+Ch, ( 2 ) 


where p = barometric pressure (in millibars) 

(1 mm Hg = 1.333 mb), 
e = water vapor pressure (mb) 

(e is of order of of p), 
temperature in degrees Kelvin, 

A = 79, R = 3.8 X 10^ C = 0.1570, D = 11, 
where Ji, the height above sea level, is measured in 
meters. 

The constants A, R, and D have been selected to get 
the best agreement with experimentally determined 
values of n. The constant (7 is 10® times the reciprocal 
of the earth’s radius in meters. A more detailed ex- 
planation of this formula is given under ^Tonstants 
of the Index of Refraction Formula” in Section 6.5.3. 

The formula (2) may be used to calculate M when 
p, T, and e are known functions of height. Nomo- 
grams have been prepared to facilitate such calcula- 
tions. In this paper tables are presented which permit 


74 


METEOROLOGY— THEORY 


these calculations to be carried out quickly and accur- 
ately. M is a number of the order of 300 to 500. 
Physically, the important quantity is the slope of M, 
i.e., dM/dh. This often calls for calculating M at fairly 
close height intervals, 15 m or even less. The values of 
M at such heights may differ by only two or three M 
units. Hence, to obtain even two significant figures 
for this quantity, the d/^s must be computed to four 
significant figures, that is, to tenths of an M unit. 
It is with a view to this situation that tables were 
computed. 

These tables fall into two groups, depending upon 
how the moisture in the atmosphere is evaluated. In 
the first group (Tables 3 to 7) the moisture is given 
in terms of relative humidity or vapor pressure ; in the 
second (Tables 8 to 11) the mixing ratio is used. 

Use of Tables 

The following examples explain the mechanics of 
using these tables. The first two examples use the first 
group of tables : Tables 3 to 7 inclusive. The quantities 
// and G which appear in these examples are auxiliary 
functions which are fully explained in the appendix. 
Examples III and IV use Tables 8 to 11. 

Example I 


Relative humidity and temperature given. 
= 1,000 (po is pressure at sea level). 


h* meters 
above 
sea level 

ec 

RH% 

W 

GM 

Md^ MJ 

Me' 


20 

13 

60 

275.6 

0.0 

275.6 41.4 

3.1 

320.1 

70 

13 

50 

274.0 

0.0 

274.0 34.5 

11.0 

319.5 

120 

15 

35 

270.5 

0.0 

270.5 27.1 

18.8 

316.4 

450 

12 

30 

262.6 

0.0 

262.6 19.5 

70.7 

352.8 

1,000 

9 

20 

248.2 

0.2 

248.4 10.9 

157.0 

416.3 

5,000 

—20 

20 

159.0 

7.0 

166.0 1.2 

785.0 

952.2 


'Columns for h (meters), t°C, and RH% give the experimentally de- 
termined data. (The heights are measured from sea level.) 

^Column for H is read from Table 3. 

is obtained by multiplying values of G given in Table 4 by 
Ai = <0 — t, where to is the air temperature at ground level. Interpolation 
is unnecessary in this table. This correction may be omitted except where 
high accuracy is desired. 

is the sum of H and GM. (If po ^ 1,000 this column should be 
multiplied by p^/ 1,000 to obtain the true Md- This, however, is necessary 
only if Po differs appreciably from 1,000 mb, since only the difference of 
refractive index from its value at the ground is of importance and this 
difference is not sensitive to moderate changes of Pq.) 

'Afjo is obtained from Table 5. 

'ikfc is obtained from Table 7 or by multiplying the column for h by 
0.1570. 

”ilf is the sum of Afd, Mw and Afg. 

^It should be noted that Po refers to the barometric pressure at sea 
level, not ground level. The difference in these quantities may be appre- 
ciable. 


Table 9, which gives pressure as a function of 
height and temperature, provides a simple method of 
calculating the sea level pressure from a measurement 
of the ground level pressure. For example, suppose 
the elevation of the ground above sea level is 100 m, 
the temperature is 15 C, and pressure at the ground 
is 993.0 mb. Table 9 shows for this height and tem- 
perature, p/p^y = 0.9882. In this case, p — 993.0, and 
hence 


V 993.0 
“ 0.9882 “ 0.9882 

Example II 


1004 . 9 . 


Vapor pressure and temperature given. 
Po= 1,000 mb at sea level. 


h* meters 
above 


sea level 

t 

e 




/ 


Me' 


10 

15.0 

10.0 

274.0 

0.0 

274.0 

4.543 

45.4 

1.6 

321.0 

40 

15.2 

9.8 

273.0 

0.0 

273.0 

4.537 

44.5 

6.3 

323.8 

75 

15.5 

9.6 

271.5 

0.0 

271.5 

4.527 

43.5 

11.8 

326.8 

150 

16.0 

9.2 

268.6 

0.0 

268.6 

4.511 

41.5 

23.6 

333.7 

300 

15.0 

9.0 

264.7 

0.0 

264.7 

4.543 

40.9 

47.1 

352.7 

1,000 

10.0 

7.0 

247.4 

0.3 

247.4 

4.706 

32.9 

157.0 

437.3 


'Columns for h, t, and e are the given data. (The heights are measured 
from sea level.) 

'^Column for H is read from Table 3. 


^GM is obtained by multiplying values of G given in Table 4 by 
At = to — t, where to = temperature at ground level. Interpolation is 
unnecessary in this table. 

is the sum of H and GAt. [if Po 7 ^ 1,000 this column should be 
multiplied by Po/ 1,000 to obtain the true Md- This correction may usually 
be omitted (see Note §, Example I).] 

"Afu, is obtained by taking the product of /, given in Table 6 , by e. 
A slide rule gives sufficiently close results here. 

^Mc is obtained from Table 7 or by multiplying the column for h by 
0.1570. 

”Af is the sum of Md, My,, and Mc> 


Example III 

Mixing ratio w and temperature given. 
Po = 1,000 mb at sea level. 


h* meters 
above sea 


level 

t 

w 

/rt 

V/Vo (p/po)F^ MJ 


20 

15 

9 

339.0 

0.9976 

338.2 

3.1 

341.3 

40 

16 

8 

330.6 

0.9953 

329.0 

6.3 

335.3 

100 

17 

7 

322.2 

0.9882 

318.4 

15.7 

334.1 

150 

17 

7 

322.2 

0.9824 

316.5 

23.6 

340.1 

300 

14 

6 

319.0 

0.9650 

307.8 

47.1 

354.9 

500 

11 

4 

307.9 

0.9420 

290.0 

78.5 

368.5 


* Columns for h, t, and w are the assumed data, w is expressed in grams 
of water vapor per kg dry air. 

F is read directly from Table 8 . 

* p is read from Table 9. In this table t means average temperature 
between ground and height h. 

(If Po 1,000 this result should be multiplied by Po/1,000. This step may 
usually be omitted.) 

® (p/Po)^ the product of the two previous columns. 

“ Me may be obtained from Table 7 or by multiplication of h by C= 0.1570. 

^ M is the sum of {p/p,^F and M^. 


COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


75 


Example IV 

Mixing ratio and temperature given. Simplified method 
satisfactory for h < 500 m.** 


versus height, below. The pressure may then be written 

( 8 ) 


p = 


h* meters 

hAu^ 

above 

sea level t w 

100 (n-l)106''M’ M 


20 

15 

9 

339.0 

0.9 

0.0 

338.1 

3.1 

341.2 

40 

16 

8 

330.6 

1.7 

0.1 

329.0 

6.3 

335.3 

100 

17 

7 

322.2 

4.0 

0.2 

318.4 

15.7 

334.1 

150 

17 

7 

322.2 

6.0 

0.3 

316.5 

23.6 

340.1 

300 

14 

6 

319.0 

11.8 

0.6 

307.8 

47.1 

354.9 

500 

11 

4 

307.9 

18.7 

1.0 

290.2 

78.5 

368.7 


where 


and 


Pq — barometric pressure at sea level, 
€ = natural logarithmic base, 
a = 0.034163, 


T^ifoTmh. 


(9) 


* Columns for h, t, and w are the assumed data. These data are the same 
as in Example 111. 

^ F is read from Table 8, as before. 

^ u is read from Table 10. 

* A« is read from Table 11. Au is then to be multiplied by h/100 to give 
the column /i Am/100, t is the average centigrade temperature from 
ground to h. 

'The column (n— 1)10® is given by F — m + A Am/100. If the average 
temperature t is negative, this column is F — m — (A Am/100). 

' Me is obtained, as before, from Table 7. M is the sum of (n— 1)10® 
and Me. 

** This method is not accurate above 500 m. It will be noted, by com- 
paring the results here with those of Example III, that there are occasional 
differences of 0.1 M units. This is due to rounding off and is not significant. 


6 . 5. 3 Procedure Used in Setting up Tables 

Tables 3 to 7 — Relative Humidity and 
Temperatuke Given 


T is thus the average temperature from ^ = 0 to the 
height h. Strictly, T should be calculated from equa- 
tion (9). However, it turns out that p is rather insen- 
sitive to T, and that, except perhaps where high accu- 
racy is desired, it is sufficient to replace equation (9) 
with 

— AT 

T = T , (10) 

2 

where AT — Tq — T and Tq is the temperature at the 
surface. 

By substituting from equations (8) and (10), equa- 
tion (4) assumes the form 


€ -«A/(r + ^r/2)^ 

For all practical cases. 


Apo 

T 


where 


may be written 

M = Md “h My, Me, 

(3) 

AT 

— « 1 

2T 

and hence. 


(4) 

,, Apo -(aA/r)[i-(Ar/2r)l 

Md= -Y ^ 

My, = Je, 

(5) 

-ahIT +(ahAT/2T^) 

= -y € • e 

Me = Ch, 

(6) 

Even at heights as great as 10^ m it can be seen that 

'' rji2 J! 

(7) 

the second of these exponentials can be replaced by the 
first two terms of its expansion. Therefore 


with 


Tables have been prepared which give the quantities 
Ma (dry term), (wet term), and Me (curvature 
term) separately. 

Dry Term. Since equation (4) contains the pressure 
p, which is not usually measured as a function of 
height, it is necessary to eliminate direct considera- 
tion of p. For this purpose a simplification of the 
elaborate formula used in the Smithsonian tables for 
calculating height as a function of pressure is suffi- 
cient. This simplification neglects very small pressure 
effects caused by humidity variations and the change 
of the acceleration of gravity with height. This prob- 
lem is discussed more fully in the section on pressure 


or 


Md +__€ -AT, 

Md = H{T,h) + G{T,h) AT, 


where 


and 


_ Apo 


H{T,h) = 
G{T,h) = 


-ahIT 


( 11 ) 


( 12 ) 


Table 3 gives the quantity H(T,h) as a function of 
h and t, where 

t = T - 27S 

is the standard centigrade temperature. In this table, 
it is assumed that po = 1,000 mb. 


76 


METEOROLOGY— THEORY 


Table 4 gives G(T,h). The term GAt in equation 
(11) is very small at altitudes less than 500 m and 
for this range of altitudes may be safely neglected. 

Since it is assumed in these tables that Pq = 1,000, 
the value of read from the tables should be multi- 
plied -by po/1,000, where Po is the actual air pressure 
at sea level. This step may, however, be eliminated in 
most cases, particularly as the physically important 
quantity is not M but differences in M at various 
heights. 

Wet Term. Since 

e = (RH)e' 
where RH = relative humidity, 

e' = saturation vapor pressure, 
and since e' is a function of temperature only, it is 
possible to prepare a table giving My, as a function of 
RH and t. This is Table 5. 

A table for f, defined by equation (7), is also in- 
cluded, so that if e is known. My, can be obtained by 
simply taking the product fe as indicated by equation 
(5) . Table 6 gives the values of /. 

Curvature Term. Table 7 gives the values of the 
linear term h/a X 10®, which must be added to obtain 
the index of refraction modified for use on a ^‘^plane 
earW^ diagram. 

Error. The discussion of this first group of tables 
is concluded with some observations on their order 
of accuracy. Theoretically any errors which arise are 
due to the expansions used in calculating M^. At a 
height as great as 10,000 m, might be, say, 70°. 
This would give G^T =13.3 for ^ = 0. If the next 
term had been included the correction would have been 
only a fraction of this amount. Since at these heights 
il/^1,800, we are safe in saying that the relative error 
is less than 0.5 per cent, probably much less than this 
amount. At altitudes of 1,000 m or less the approxima- 
tion introduces errors too small to be reflected in the 
fourth significant figure. 

Aside from this theoretical error, there are errors 
in the table due to rounding off in the numerical work. 
An effort was made to keep this error less than 0.1 
M units. 

Tables 8 to 11 — Mixing Ratio and 
Temperature Given 

In terms of atmospheric pressure and water vapor 
pressure, the mixing ratio w is given by 

^ = ( 13 ) 

p — e 

Since w involves the pressure p, the scheme used in 


the first group of tables must be modified. Using 
equation (13), equation (2) assumes the form 


M^'^F{T,w) + Ch, (14) 

Vo 

where 

+ in?® (?-.-?)■ 

Table 8 gives F for the range of usable values of 
temperature and mixing ratio. Since F is sensitive 
to variations in both T and w, the tabulation is made 
for all integral values of both T and w to avoid labori- 
ous interpolation. 

Following the procedure used in the discussion of 
dry term in Section 6.5.3, the pressure p is calculated 
from equation (8). These results are given in Table 
9. In view of the insensitivity of p to T, the average 
temperature, it is unnecessary to tabulate p for all 
values of T; it is sufficient to tabulate p at 5-degree 
intervals of T. 

The term Ch has been calculated in connection with 
the first group of tables and is given in Table 7. 


Tables 10 and 11 for Use at Low Altitudes 
An objectionable feature of the method given in 
the preceding section is that it involves taking the 
product, pF, which makes an application of the tables 
rather slow. The following method circumvents this 
difficulty for heights less than 500 m. From equations 
(1), (8), and (15) 


(n - 1) 10® = Fe . (16) 

For altitudes of less than 500 m it is safe to sup- 
pose that 

ah ah / t 

T 273 \ 273 

where 1 is the average centigrade temperature, and 
that 


^ -ahiT = g -ahms . ^ _J_ ahil{21Z)^ _ ^ -ahl273 


+ 


ahi 

( 2 ^ 2 '- 

(n - 1)10" = F - M + ^ , 
u = F{1 - 

A 

“ “ ( 273 ) 2 ' 

Equation (19) is evaluated in Table 10. 


-aA/273 


Hence 

where 

and 


(17) 

(18) 

(19) 

( 20 ) 


COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


77 


Equation (20) is a small correction which must be 
taken into account when t, the average temperature, 
differs appreciably from zero. Since this term con- 
tributes only 1 per cent to the refractive index in the 
extreme case oi h = 500 m, ^ = 40, it is sufficient to 
replace the exponential by its value at the middle of 
the height range. This approximation does not lead 
to an error of more than 0.1 M units at these low 
altitudes. 


Pkessure versus Height 

The differential equation connecting height with 
pressure may be written 

dp g dh , , 

p B T ’ 

where g = acceleration of gravity, 

R = gas constant for air. 

Since g is not strictly constant (it varies slightly with 
height and locality) and since R, to a slight extent, is 
dependent on the percentage of water vapor in the 
air and, finally, since T may be an arbitrary function 
of height, this differential equation cannot be inte- 
grated exactly. However, a careful consideration of the 
order of magnitude of changes in the pressure brought 
about by the slight changes of g and R leads to the 
conclusion that such variations may be neglected, 
particularly as these changes have practically no effect 
on the slopes of M curves. Picking the best overall 
values of g and R {g = 9.80665 and R = 287.05 in 
the units used in this report) ' gives (x = g/R = 
0.034163 as the value to be used in equation (8). 

The variation of temperature with height cannot, 
however, be neglected in the integration of equation 
(21). The integrated form of equation (21) is equa- 
tion (8), where the approximation 



(22) 


has been made. T is the average temperature defined 
by equation (9) or, more roughly, by equation (10). 

An estimate of the order of accuracy of this approxi- 
mation may be obtained from an examination of the 
case in which T varies linearly with h. Let the refer- 
ence level temperature he h = 0 and the tem- 

perature at the height be T^. Then 


^ ^ 2hi 

T~ To -\-Ti 


(23) 


and, for this linear case 


dh _ 
0 T 



Ti 

To 


2h pi- To 1/ Ti-To y 1 
Ti-ToLTi+To^ 3VTi-hTo/ “ J 

(24) 


by a well-known expansion for the natural logarithm. 
The first term in the series (24) gives exactly equation 
(23). Hence, the approximation (22) amounts to 
dropping the higher-order terms in equation (24). 
The ratio of the second term to the first is only 
Vs [(Ti — Tq)/{Tj^-\- Tq)Y or about two parts in 
10,000 for the first 2,000 m of the standard atmos- 
phere. This comes out to give an error of about 0.006 
mb in the pressure at this height. This is certainly 
negligible. 

For a nonlinear atmosphere the question of the 
error in equation (22) is chiefly a question of the 
accuracy in determining T, since any such atmosphere 
can be broken up into a number of layers in each of 
which T is linear in h. 


Constants of the Index of Refraction 
Formula 

The formula for the ordinary index of refraction, 
n, which has been used in calculating these tables, is 

(„_l)10e = 4P-?l+^, (25) 

^ ^ TP T^ ^ ' 

where A = 79, D = 11, R = 3.8 X 10^ (26) 

The formula given in reference 11, in the units 
adopted here, is the same as (25) but with 

A = 78.7, D = 11.2, B = 3.77 X 10^ (27) 

The formula used by Bell Telephone Laboratories 
(Monograph B-870, 1935) is also (25) but with 

A = 79.1, D= 10.9, B = 3.81 X 10^ (28) 

The third significant figure in all these constants 
is questionable. Moreover, the absolute value of n 
(or M) is not important but only the slopes of M 
curves. For this purpose it is sufficient if the right 
form of equation and approximately correct values of 
the constants are chosen. Hence, in these tables, equa- 
tions (25) and (26) were adopted. 


78 


METEOROLOGY— THEORY 


Table 3A. H for t from -30 C (-22 F) to -20 C (-4 F); /i to 2,000 m (6,562 ft). 


'Pq = 1,000 mb at sea level 

Vc^ / 


A(m)\ 

-30 

-29 

-28 

-27 

-26 

-25 

-24 

-23 

-22 

-21 

-20 

/h (ft) 


325.1 

323.8 

322.4 

321.1 

319.8 

318.5 

317.3 

316.0 

314.7 

313.5 

312.3 

0.0 

10 

324.6 

323.3 

322.0 

320.7 

319.4 

318.1 

316.9 

315.6 

314.3 

313.1 

311.9 

32.8 

20 

324.2 

322.9 

321.5 

320.3 

319.0 

317.7 

316.5 

315.2 

313.9 

312.7 

311.5 

65.6 

30 

323.7 

322.4 

321.1 

319.8 

318.5 

317.2 

316.0 

314.7 

313.5 

312.2 

311.0 

98.4 

40 

323.3 

322.0 

320.6 

319.4 

318.1 

316.8 

315.6 

314.3 

313.1 

311.8 

310.6 

131.2 

50 

322.8 

321.5 

320.2 

319.0 

317.7 

316.4 

315.2 

313.9 

312.7 

311.4 

310.2 

164.0 

75 

321.7 

320.4 

319.1 

317.9 

316.6 

315.3 

314.1 

312.9 

311.6 

310.4 

309.2 

248.1 

100 

320.6 

319.3 

318.0 

316.8 

315.5 

314.2 

313.0 

311.8 

310.5 

309.3 

308.1 

328.1 

150 

318.3 

317.0 

315.8 

314.5 

313.3 

312.0 

310.8 

309.6 

308.4 

307.2 

306.0 

492.1 

200 

316.1 

314.9 

313.6 

312.4 

311.1 

309.9 

308.7 

307.5 

306.3 

305.1 

303.9 

656.2 

250 

313.9 

312.7 

311.5 

310.2 

309.0 

307.8 

306.6 

305.4 

304.3 

303.1 

301.9 

820.2 

300 

311.7 

310.5 

309.3 

308.0 

306.8 

305.6 

304.5 

303.3 

302.2 

301.0 

299.9 

984.3 

350 

309.5 

308.3 

307.1 

305.9 

304.7 

303.5 

302.4 

301.2 

300.1 

298.9 

297.8 

1,148.0 

400 

307.3 

306.1 

305.0 

303.8 

302.7 

301.5 

300.4 

299.2 

298.1 

296.9 

295.8 

1,312.0 

450 

305.2 

304.0 

302.9 

301.7 

300.6 

299.4 

298.3 

297.2 

296.0 

294.9 

293.8 

1,476.0 

500 

303.0 

301.9 

300.7 

299.6 

298.4 

297.3 

296.2 

295.1 

294.1 

293.0 

291.9 

1,640.0 

600 

298.8 

297.7 

296.6 

295.5 

294.4 

293.3 

292.2 

291.2 

290.1 

289.1 

288.0 

1,969.0 

700 

294.6 

293.5 

292.5 

291.4 

290.4 

289.3 

288.3 

287.2 

286.2 

285.1 

284.1 

2,297.0 

800 

290.5 

289.5 

288.4 

287.4 

286.3 

285.3 

284.3 

283.3 

282.3 

281.3 

280.3 

2,625.0 

900 

286.5 

285.5 

284.5 

283.4 

282.4 

281.4 

280.4 

279.4 

278.5 

277.5 

276.5 

2,953.0 

1,000 

282.5 

281.5 

280.5 

279.5 

278.5 

277.5 

276.6 

275.6 

274.7 

273.7 

272.8 

3,281.0 

1,500 

263.3 

262.5 

261.6 

260.8 

259.9 

259.1 

258.3 

257.5 

256.6 

255.8 

255.0 

4,921.0 

2,000 

245.4 

244.7 

244.0 

243.2 

242.5 

241.8 

241.1 

240.4 

239.7 

239.0 

238.3 

6,562.0 


-22.0 

-20.2 

-18.4 

-16.6 

-14.8 

-13.0 

-11.2 

-9.40 

-7.60 

-5.80 

-4.00 

\ h (ft) 

<f\ 


\tc 

h(m)\ 

-20 

Table 3B. H for t from 

-19 -18 -17 

-20 C (-4 F) to - 
po = 1,000 mb at 

-16 -15 

-10 C ( + 14 F); to 2,000 

sea level 

-14 -13 -12 

m (6,562 ft). 

-11 -10 

/Mft) 


312.3 

311.0 

309.8 

308.6 

307.4 

306.2 

305.0 

303.8 

302.7 

301.5 

300.4 

0.0 

10 

311.9 

310.6 

309.4 

308.2 

307.0 

305.8 

304.6 

303.4 

302.3 

301.1 

300.0 

32.8 

20 

311.5 

310.2 

309.0 

307.8 

306.6 

305.4 

304.2 

303.0 

301.9 

300.7 

299.6 

65.6 

30 

311.0 

309.8 

308.6 

307.4 

306.2 

305.0 

303.8 

302.7 

301.5 

300.4 

299.2 

98.4 

40 

310.6 

309.4 

308.2 

307.0 

305.8 

304.6 

303.4 

302.3 

301.1 

300.0 

298.8 

131.2 

50 

310.2 

309.0 

307.8 

306.6 

305.4 

304.2 

303.0 

301.9 

300.7 

299.6 

298.4 

164.0 

75 

309.2 

308.0 

306.8 

305.6 

304.4 

303.2 

302.1 

300.9 

299.8 

298.6 

295.5 

248.1 

100 

308.1 

306.9 

305.7 

304.6 

303.4 

302.2 

301.1 

299.9 

298.8 

297.6 

296.5 

328.1 

150 

306.0 

304.8 

303.6 

302.5 

301.3 

300.1 

299.0 

297.9 

296.8 

295.7 

294.6 

492.1 

200 

303.9 

302.8 

301.6 

300.5 

299.3 

298.2 

297.1 

296.0 

294.9 

293.8 

292.7 

656.2 

250 

301.9 

300.8 

299.6 

298.5 

297.3 

296.2 

295.1 

294.0 

293.0 

291.9 

290.8 

820.2 

300 

299.9 

298.8 

297.7 

296.5 

295.4 

294.3 

293.2 

292.1 

291.1 

290.0 

288.9 

984.3 

350 

297.8 

296.7 

295.6 

294.5 

293.4 

292.3 

291.2 

290.2 

289.1 

288.1 

287.0 

1,148.0 

400 

295.8 

294.7 

293.6 

292.6 

291.5 

290.4 

289.4 

288.3 

287.3 

286.2 

285.2 

1,312.0 

450 

293.8 

292.7 

291.7 

290.6 

289.6 

288.5 

287.5 

286.4 

285.4 

284.3 

283.3 

1,476.0 

500 

291.9 

290.8 

289.8 

288.7 

287.7 

286.6 

285.6 

284.6 

283.5 

282.5 

281.5 

1,640.0 

600 

288.0 

287.0 

285.9 

284.9 

283.8 

282.8 

281.8 

280.8 

279.9 

278.9 

277.9 

1,969.0 

700 

284.1 

283.1 

282.1 

281.1 

280.1 

279.1 

278.1 

277.2 

276.2 

275.3 

274.3 

2,297.0 

800 

280.3 

279.3 

278.3 

277.4 

276.4 

275.4 

274.5 

273.5 

272.6 

271.6 

270.7 

2,625.0 

900 

276.5 

275.5 

274.6 

273.7 

272.7 

271.8 

270.9 

270.0 

269.0 

268.1 

267.2 

2,953.0 

1,000 

272.8 

271.9 

271.0 

270.0 

269.1 

268.2 

267.3 

266.4 

265.6 

264.7 

263.8 

3,281.0 

1,500 

255.0 

254.2 

253.4 

252.6 

251.8 

251.0 

250.2 

249.5 

248.7 

248.0 

247.2 

4,921.0 

2,000 

238.3 

237.6 

237.0 

236.3 

235.7 

235.0 

234.3 

233.7 

233.0 

232.4 

231.7 

6562.0 


-4.00 

-2.20 

-0.40 

+ 1.40 

+ 3.20 

+ 5.00 

+ 6.80 

+ 8.60 

+ 10.4 

+ 12.2 

+ 14.00 

\A (ft) 


I f\ 


COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


79 


Table 3 C . H for t from - 10 C ( + 14 F ) to 0 C (32 F ); to 2,000 m (6,562 ft). 

po = 1,000 mb at sea level 




h ( m ) \ 

-10 

-9 

-8 

-7 

-6 

-5 

-4 

-3 

-2 

-1 

±0 

/ h ( ft ) 


300.4 

299.2 

298.1 

297.0 

295.9 

294.8 

293.7 

292.6 

291.5 

290.4 

289.4 

0.0 

10 

300.0 

298.8 

297.7 

296.6 

295.5 

294.4 

293.3 

292.2 

291.1 

290.1 

289.0 

32.8 

20 

299.6 

298.4 

297.3 

296.2 

295.1 

294.0 

292.9 

291.9 

290.8 

289.7 

288.7 

65.6 

30 

299.2 

298.1 

297.0 

295.9 

294.8 

293.7 

292.6 

291.5 

290.4 

289.4 

288.3 

98.4 

40 

298.8 

297.7 

296.6 

295.5 

294.4 

293.3 

292.2 

291.2 

290.1 

289.0 

288.0 

131.2 

50 

298.4 

297.3 

296.2 

295.1 

294.0 

292.9 

291.8 

290.8 

289.7 

288.7 

287.6 

164.0 

75 

295.5 

296.3 

295.2 

294.1 

293.0 

291.9 

290.8 

289.8 

288.7 

287.7 

286.6 

248.1 

100 

296.5 

295.4 

294.3 

293.3 

292.2 

291.1 

290.0 

289.0 

287.9 

286.9 

285.8 

328.1 

150 

294.6 

293.5 

292.4 

291.4 

290.3 

289.2 

288.2 

287.1 

286.1 

285.0 

284.0 

492.1 

200 

292.7 

291.6 

290.5 

289.5 

288.4 

287.3 

286.3 

285.3 

284.2 

283.2 

282.2 

656.2 

250 

290.8 

289.7 

288.7 

287.6 

286.6 

285.5 

284.5 

283.5 

282.5 

281.5 

280.5 

820.2 

300 

288.9 

287.9 

286.8 

285.8 

284.7 

283.7 

282.7 

281.7 

280.7 

279.7 

278.7 

984.3 

350 

287.0 

286.0 

285.0 

283.9 

282.9 

281.9 

280.9 

279.9 

279.0 

278.0 

277.0 

1,148.0 

400 

285.2 

284.2 

283.2 

282.1 

281.1 

280.1 

279.1 

278.2 

277.2 

276.3 

275.3 

1,312.0 

450 

283.3 

282.3 

281.3 

280.3 

279.3 

278.3 

277.3 

276.4 

275.4 

274.5 

273.5 

1,476.0 

500 

281.5 

280.5 

279.5 

278.6 

277.6 

276.6 

275.6 

274.7 

273.7 

272.8 

271.8 

1,640.0 

600 

277.9 

276.9 

276.0 

275.0 

274.1 

273.1 

272.2 

271.3 

270.3 

269.4 

268.5 

1,969.0 

700 

274.3 

273.4 

272.4 

271.5 

270.5 

269.6 

268.7 

267.8 

266.9 

266.0 

265.1 

2,297.0 

800 

270.7 

269.8 

268.9 

268.0 

267.1 

266.2 

265.3 

264.4 

263.6 

262.7 

261.8 

2,625.0 

900 

267.2 

266.3 

265.4 

264.6 

263.7 

262.8 

262.0 

261.1 

260.3 

259.4 

258.6 

2,953.0 

1,000 

263.8 

262.9 

262.1 

261.2 

260.4 

259.5 

258.7 

257.8 

257.0 

256.1 

255.3 

3,281.0 

1,500 

247.2 

246.5 

245.7 

245.0 

244.2 

243.5 

242.8 

242.1 

241.3 

240.6 

239.9 

4,921.0 

2,000 

231.7 

231.0 

230.4 

229.7 

229.1 

228.4 

227.8 

227.2 

226.5 

225.9 

225.3 

6,562.0 


14.0 

15.8 

17.6 

19.4 

21.2 

23.0 

24.8 

26.6 

28.4 

30.2 

32.0 

\/i ( ft ) 


< F \ 

Table 3 D . H for t from 0 C (32 F ) to 10 C (50 F ); h to 2,000 m (6,562 ft). 

po = 1,000 mb at sea level 


h { m )\ 

±0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

/A ( ft ) 


289.4 

288.3 

287.3 

286.2 

285.2 

284.2 

283.2 

282.1 

281.1 

280.1 

279.2 

0.0 

10 

289.0 

288.0 

286.9 

285.9 

284.8 

283.8 

282.8 

281.8 

280.8 

279.8 

278.9 

32.8 

20 

288.7 

287.6 

286.6 

285.5 

284.5 

283.5 

282.5 

281.4 

280.5 

279.5 

278.5 

65.6 

30 

288.3 

287.3 

286.2 

285.2 

284.1 

283.1 

282.1 

281.1 

280.1 

279.1 

278.2 

98.4 

40 

288.0 

286.9 

285.9 

284.8 

283.8 

282.8 

281.8 

280.7 

279.8 

278.8 

277.8 

131.2 

50 

287.6 

286.6 

285.5 

284.5 

283.4 

282.4 

281.4 

280.4 

279.5 

278.5 

277.5 

164.0 

75 

286.6 

285.7 

284.7 

283.6 

282.6 

281.6 

280.6 

279.6 

278.7 

277.7 

276.7 

248.1 

100 

285.8 

284.8 

283.8 

282.7 

281.7 

280.7 

279.7 

278.7 

277.8 

276.8 

275.8 

328.1 

150 

284.0 

283.0 

282.0 

281.0 

280.0 

279.0 

278.0 

277.1 

276.1 

275.2 

274.2 

492.1 

200 

282.2 

281.2 

280.2 

279.3 

278.3 

277.3 

276.3 

275.4 

274.4 

273.5 

272.5 

656.2 

250 

280.5 

279.5 

278.5 

277.6 

276.6 

275.6 

274.7 

273.7 

272.8 

271.8 

270.9 

820.2 

300 

278.7 

277.7 

276.8 

275.8 

274.9 

273.9 

273.0 

272.0 

271.1 

270.1 

269.2 

984.3 

350 

277.0 

276.0 

275.1 

274.1 

273.2 

272.2 

271.3 

270.4 

269.4 

268.5 

267.6 

1,148.0 

400 

275.3 

274.3 

273.4 

272.4 

271.5 

270.5 

269.6 

268.7 

267.8 

266.9 

266.0 

1,312.0 

450 

273.5 

272.6 

271.7 

270.7 

269.8 

268.9 

268.0 

267.1 

266.2 

265.3 

264.4 

1,476.0 

500 

271.8 

270.9 

270.0 

269.0 

268.1 

267.2 

266.3 

265.4 

264.6 

263.7 

262.8 

1,640.0 

600 

268.5 

267.6 

266.7 

265.8 

264.9 

264.0 

263.1 

262.2 

261.4 

260.5 

259.6 

1,969.0 

700 

265.1 

264.2 

263.4 

262.5 

261.7 

260.8 

259.9 

259.1 

258.2 

257.4 

256.5 

2,297.0 

800 

261.8 

260.9 

260.1 

259.2 

258.4 

257.5 

256.7 

255.9 

255.0 

254.2 

253.4 

2,625.0 

900 

258.6 

257.8 

256.9 

256.1 

255.2 

254.4 

253.6 

252.8 

252.0 

251.2 

250.4 

2,953.0 

1,000 

255.3 

254.5 

253.7 

252.9 

252.1 

251.3 

250.5 

249.7 

249.0 

248.2 

247.4 

3,281.0 

1,500 

239.9 

239.2 

238.5 

237.7 

237.0 

236.3 

235.6 

234.9 

234.3 

233.6 

232.9 

4,921.0 

2,000 

225.3 

224.7 

224.1 

223.5 

222.9 

222.3 

221.7 

221.1 

220.5 

219.9 

219.3 

6,562.0 


32.0 

33.8 

35.6 

37.4 

39.2 

41.0 

42.8 

44.6 

46.4 

48.2 

50.0 

\/i ( ft ) 

/ F \ 


80 


METEOROLOGY— THEORY 


Table 3E. H for t from 10 C (50 F) to 20 C (68 F); h to 2,000 m (6,562 ft). 

po = 1,000 mb at sea level 


tC y/ 


h (m) \ 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

/h (ft) 


279.2 

278.2 

277.2 

276.2 

275.3 

274.3 

273.4 

272.4 

271.5 

270.5 

269.6 

0.0 

10 

278.9 

277.9 

276.9 

275.9 

274.9 

274.0 

273.1 

272.1 

271.2 

270.2 

269.3 

32.8 

20 

278.5 

277.5 

276.6 

275.6 

274.6 

273.7 

272.8 

271.8 

270.9 

269.9 

269.0 

65.6 

30 

278.2 

277.2 

276.2 

275.2 

274.3 

273.3 

272.4 

271.5 

270.5 

269.6 

268.7 

98.4 

40 

277.8 

276.8 

275.9 

274.9 

274.0 

273.0 

272.1 

271.2 

270.2 

269.3 

268.4 

131.2 

50 

277.5 

276.5 

275.6 

274.6 

273.7 

272.7 

271.8 

270.9 

269.9 

269.0 

268.1 

164.0 

75 

276.7 

275.7 

274.8 

273.8 

272.8 

271.9 

271.0 

270.1 

269.1 

268.2 

267.3 

248.1 

100 

275.8 

274.9 

273.9 

273.0 

272.0 

271.1 

270.2 

269.3 

268.3 

267.4 

266.5 

328.1 

150 

274.2 

273.3 

272.3 

271.4 

270.4 

269.5 

268.6 

267.7 

266.8 

265.9 

265.0 

492.1 

200 

272.5 

271.6 

270.7 

269.7 

268.8 

267.9 

267.0 

266.1 

265.2 

264.3 

263.4 

656.2 

250 

270.9 

270.0 

269.1 

268.1 

267.2 

266.3 

265.4 

264.5 

263.7 

262.8 

261.9 

820.2 

300 

269.2 

268.3 

267.4 

266.5 

265.6 

264.7 

263.8 

262.9 

262.1 

261.2 

260.3 

984.3 

350 

267.6 

266.7 

265.8 

264.9 

264.0 

263.1 

262.2 

261.4 

260.5 

259.7 

258.8 

1,148.0 

400 

266.0 

265.1 

264.2 

263.4 

262.5 

261.6 

260.7 

259.9 

259.0 

258.2 

257.3 

1,312.0 

450 

264.4 

263.5 

262.6 

261.8 

260.9 

260.0 

259.2 

258.3 

257.5 

256.6 

255.8 

1,476.0 

500 

262.8 

261.9 

261.1 

260.2 

259.4 

258.5 

257.7 

256.9 

256.0 

255.2 

254.4 

1,640.0 

600 

259.6 

258.8 

258.0 

257.1 

256.3 

255.5 

254.7 

253.9 

253.0 

252.2 

251.4 

1,969.0 

700 

256.5 

255.7 

254.9 

254.0 

253.2 

252.4 

251.6 

250.8 

250.1 

249.3 

248.5 

2,297.0 

800 

253.4 

252.6 

251.8 

251.1 

250.3 

249.5 

248.7 

247.9 

247.2 

246.4 

245.6 

2,625.0 

900 

250.4 . 

249.6 

248.8 

248.1 

247.3 

246.5 

245.8 

245.0 

244.3 

243.5 

242.8 

2,953.0 

1,000 

247.4 - 

246.6 

245.9 

245.1 

244.4 

243.6 

242.9 

242.1 

241.4 

240.6 

239.9 

3,281.0 

1,500 

232.9,. 

232.2 

231.6 

230.9 

230.3 

229.6 

228.9 

228.3 

227.6 

227.0 

226.3 

4,921.0 

2,000 

219.3 

218.7 

218.1 

217.6 

217.0 

216.4 

215.8 

215.2 

214.7 

214.1 

213.5 

6,562.0 


50.0 

51.8 

53.6 

55.4 

57.2 

59.0 

60.8 

62.6 

64.4 

66.2 

68.0 (ft) 


IF \ 


Table 3F. H for I from 20 C (68 F) to 30 C (86 F); h to 2,000 m (6,562 ft). 

Po = 1,000 mb at sea level 


\ (C^ 
h (m)\ 20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

yh (ft) 

1 0 

269.6 

268.7 

267.8 

266.9 

266.0 

265.1 

264.2 

263.3 

262.5 

261.6 

260.7 

0.0 

10 

269.3 

268.4 

267.5 

266.6 

265.7 

264.8 

263.9 

263.0 

262.2 

261.3 

260.4 

32.8 

20 

269.0 

268.1 

267.2 

266.3 

265.4 

264.5 

263.6 

262.7 

261.9 

261.0 

260.1 

65.6 

30 

268.7 

267.8 

266.9 

266.0 

265.1 

264.2 

263.3 

262.5 

261.6 

260.8 

259.9 

98.4 

40 

268.4 

267.5 

266.6 

265.7 

264.8 

263.9 

263.0 

262.2 

261.3 

260.5 

259.6 

131.2 

50 

268.1 

267.2 

266.3 

265.4 

264.5 

263.6 

262.7 

261.9 

261.0 

260.2 

259.3 

164.0 

75 

267.3 

266.4 

265.5 

264.7 

263.8 

262.9 

262.0 

261.2 

260.3 

259.5 

258.6 

248.1 

100 

266.5 

265.6 

264.7 

263.9 

263.0 

262.1 

261.2 

260.4 

259.5 

258.7 

257.8 

328.1 

150 

265.0 

264.1 

263.2 

262.4 

261.5 

260.6 

259.7 

258.9 

258.0 

257.2 

256.3 

492.1 

200 

263.4 

262.5 

261.7 

260.8 

260.0 

259.1 

258.3 

257.4 

256.6 

255.7 

254.9 

656.2 

250 

261.9 

261.0 

260.2 

259.3 

258.5 

257.6 

256.8 

256.0 

255.1 

254.3 

253.5 

820.2 

300 

260.3 

259.5 

258.6 

257.8 

256.9 

256.1 

255.3 

254.5 

253.6 

252.8 

252.0 

984.3 

350 

258.8 

258.0 

257.2 

256.3 

255.5 

254.7 

253.9 

253.1 

252.2 

251.4 

250.6 

1,148.0 

400 

257.3 

256.5 

255.7 

254.8 

254.0 

253.2 

252.4 

251.6 

250.8 

250.0 

249.2 

1,312.0 

450 

255.8 

255.0 

254.2 

253.4 

252.6 

251.8 

251.0 

250.2 

249.4 

248.6 

247.8 

1,476.0 

500 

254.4 

253.6 

252.8 

251.9 

251.1 

250.3 

249.5 

248.7 

248.0 

247.2 

246.4 

1,640.0 

600 

251.4 

250.6 

249.8 

249.1 

248.3 

247.5 

246.7 

246.0 

245.2 

244.5 

243.7 

1,969.0 

700 

248.5 

247.7 

247.0 

246.2 

245.5 

244.7 

243.9 

243.2 

242.4 

241.7 

240.9 

2,297.0 

800 

245.6 

244.9 

244.1 

243.4 

242.6 

241.9 

241.2 

240.5 

239.7 

239.0 

238.3 

2,625.0 

900 

242.8 

242.1 

241.3 

240.6 

239.8 

239.1 

238.4 

237.7 

237.0 

236.3 

235.6 

2,953.0 

1,000 

239.9 

239.2 

238.5 

237.8 

237.1 

236.4 

235.7 

235.0 

234.3 

233.6 

232.9 

3,281.0 

1,500 

226.3 

225.7 

225.1 

224.4 

223.8 

223.2 

222.6 

222.0 

221.4 

220.8 

220.2 

4,921.0 

2,000 

213.5 

213.0 

212.4 

211.9 

211.3 

210.8 

210.3 

209.7 

209.2 

208.6 

208.1 

6,562.0 


86.0 

87.8 

89.6 

91.4 

93.2 

95.0 

96.8 

98.6 

100.4 

102.2 

104.0 

\/i (ft) 


( F\ 


COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


81 


Table 3G. H for t from 30 C (86 F) to 40 C (104 F); h to 2,000 m (6,562 ft). 
po = 1,000 mb at sea level 


h (m)\ 30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

h (ft) 

1 0 

260.7 

259.9 

259.0 

258.2 

257.5 

256.5 

255.7 

254.8 

254.0 

253.2 

252.4 

0.0 

10 

260.4 

259.6 

258.7 

257.9 

257.2 

256.2 

255.4 

254.5 

253.7 

252.9 

252.1 

32.8 

20 

260.1 

259.3 

258.4 

257.6 

256.9 

255.9 

255.1 

254.3 

253.4 

252.6 

251.8 

65.6 

30 

259.9 

259.1 

258.2 

257.4 

256.5 

255.7 

254.9 

254.0 

253.2 

252.4 

251.6 

98.4 

40 

259.6 

258.8 

257.9 

257.1 

256.2 

255.4 

254.6 

253.8 

252.9 

252.1 

251.3 

131.2 

50 

259.3 

258.5 

257.6 

256.8 

255.9 

255.1 

254.3 

253.5 

252.6 

251.8 

251.0 

164.0 

75 

258.6 

257.7 

256.9 

256.0 

254.2 

254.4 

253.6 

252.8 

251.9 

251.1 

250.3 

248.1 

100 

257.8 

257.0 

256.2 

255.3 

254.5 

253.7 

252.9 

252.1 

251.3 

250.5 

249.7 

328.1 

150 

256.3 

255.5 

254.7 

253.9 

253.1 

252.3 

251.5 

250.7 

249.9 

249.1 

248.3 

492.1 

200 

254.9 

254.1 

253.3 

252.5 

251.7 

250.9 

250.1 

249.3 

248.5 

247,7 

246.9 

656.2 

250 

253.5 

252.7 

251.9 

251.1 

250.3 

249.5 

248.7 

247.9 

247.2 

246.4 

245.6 

820.2 

300 

252.0 

251.2 

250.4 

249.7 

248.9 

248.1 

247.3 

246.6 

245.8 

245.1 

244.3 

984.3 

350 

250.6 

249.8 

249.0 

248.3 

247.5 

246.7 

245.9 

245.2 

244.4 

243.7 

242.9 

1,148.0 

400 

249.2 

248.4 

247.7 

246.9 

246.2 

245.4 

244.6 

243.9 

243.1 

242.4 

241.6 

1,312.0 

450 

247.8 

247.0 

246.3 

245.5 

244.8 

244.0 

243.3 

242.5 

241.8 

241.0 

240.3 

1,476.0 

500 

246.4 

245.6 

244.9 

244.1 

243.4 

242.6 

241.9 

241.2 

240.4 

239.7 

239.0 

1,640.0 

600 

243.7 

242.9 

242.2 

241.4 

240.7 

239.9 

239.2 

238.5 

237.8 

237.1 

236.4 

1,969.0 

700 

240.9 

240.2 

239.5 

238.7 

238.0 

237.3 

236.6 

235.9 

235.2 

234.5 

233.8 

2,297.0 

800 

238.3 

237.6 

236.9 

236.1 

235.4 

234.7 

234.0 

233.3 

232.7 

232.0 

231.3 

2,625.0 

900 

235.6 

234.9 

234.2 

233.5 

232.8 

232.1 

231.4 

230.8 

230.1 

229.5 

228.8 

2,953.0 

1,000 

232.9 

232.2 

231.6 

230.9 

230.3 

229.6 

228.9 

228.3 

227.6 

227.0 

226.3 

3,281.0 

1,500 

220.2 

219.6 

219.0 

218.4 

217.8 

217.2 

216.6 

216.0 

215.5 

214.9 

214.3 

4,921.0 

2,000 

208.1 

207.6 

207.1 

206.5 

206.0 

205.5 

205.0 

204.5 

203.9 

203.4 

202.9 

6,562.0 


86.0 

87.9 

89.6 

91.4 

93.2 

95.0, 

96.8 

98.6 

100.4 

102.2 

104.0 

\/i (ft) 


tF \ 


Table 4. G for h from 50 m (164 ft) to 2,000 m (6,562 ft) and t from —30 C (—22 F) to 40 C (104 F). 


\<C 
h (m)\ 

-30 

-25 

-20 

-15 

-10 

-5 

±0 

+ 5 

+ 10 

+ 15 

+ 20 

+25 

+30 

+35 

+40 

/ 

yh { h ) 

i 50 

0.005 

0.004 

0.004 

0.004 

0.004 

0.003 

0.003 

0.003 

0.003 

0.003 

0.003 

0.003 

0.002 

0.002 

0.002 

164.0 

100 

0.009 

0.009 

0.008 

0.008 

0.007 

0.007 

0.007 

0.006 

0.006 

0.006 

0.005 

0.005 

0.005 

0.005 

0.004 

328.1 

150 

0.014 

0.013 

0.012 

0.012 

0.011 

0.010 

0.010 

0.009 

0.009 

0.008 

0.008 

0.008 

0.007 

0.007 

0.006 

492.1 

200 

0.018 

0.017 

0.016 

0.015 

0.014 

0.014 

0.013 

0.012 

0.012 

0.011 

0.010 

0.010 

0.009 

0.009 

0.009 

656.2 

250 

0.023 

0.021 

0.020 

0.019 

0.018 

0.017 

0.016 

0.015 

0.014 

0.014 

0.013 

0.012 

0.012 

0.011 

0.011 

820.2 

300 

0.027 

0.025 

0.024 

0.023 

0.021 

0.020 

0.019 

0.018 

0.017 

0.016 

0.016 

0.015 

0.014 

0.013 

0.013 

984.3 

350 

0.031 

0.030 

0.028 

0.026 

0.025 

0.023 

0.022 

0.021 

0.020 

0.019 

0.018 

0.017 

0.016 

0.016 

0.015 

1,148.0 

400 

0.036 

0.033 

0.032 

0.030 

0.028 

0.027 

0.025 

0.024 

0.023 

0.022 

0.020 

0.019 

0.019 

0.018 

0.017 

1,312.0 

450 

0.040 

0.037 

0.035 

0.033 

0.031 

0.030 

0.028 

0.027 

0.025 

0.024 

0.023 

0.022 

0.021 

0.020 

0.019 

1,476.0 

500 

0.044 

0.041 

0.039 

0.037 

0.035 

0.033 

0.031 

0.030 

0.028 

0.027 

0.025 

0.024 

0.023 

0.022 

0.021 

1,640.0 

600 

0.052 

0.049 

0.046 

0.044 

0.041 

0.039 

0.037 

0.035 

0.033 

0.032 

0.030 

0.029 

0.027 

0.026 

0.025 

1,969.0 

700 

0.060 

0.056 

0.053 

0.050 

0.047 

0.045 

0.043 

0.040 

0.038 

0.036 

0.035 

0.033 

0.031 

0.030 

0.029 

2,297.0 

800 

0.067 

0.063 

0.060 

0.057 

0.053 

0.051 

0.048 

0.046 

0.043 

0.041 

0.039 

0.037 

0.035 

0.034 

0.032 

2,625.0 

900 

0.075 

0.070 

0.066 

0.063 

0.059 

0.056 

0.053 

0.051 

0.048 

0.046 

0.043 

0.041 

0.039 

0.038 

0.036 

2,953.0 

1,000 

0.082 

0.077 

0.073 

0.069 

0.065 

0.062 

0.059 

0.056 

0.053 

0.050 

0.048 

0.045 

0.043 

0.041 

0.039 

3,281.0 

1,500 

0.114 

0.108 

0.102 

0.097 

0.092 

0.087 

0.082 

0.078 

0.075 

0.071 

0.068 

0.064 

0.061 

0.059 

0.056 

4,921.0 

2,000 

0.142 

0.134 

0.127 

0.121 

0.114 

0.109 

0.103 

0.098 

0.094 

0.089 

0.085 

0.081 

0.077 

0.074 

0.071 

6,562.0 


-22.0 - 

-13.0 

-4.0 

+ 5.0 

14.0 

23.0 

32.0 

41.0 

50.0 

59.0 

68.0 

77.0 

86.0 

95.0 

104.0 

\<F 


Table 5. M , j , for t from -30 C (-22 F) to 40 C (104 F). 



10 

20 

30 

40 

Relative humidity 
50 60 

70 

80 

90 

100 


-30 

0.2 

0.5 

0.7 

1.0 

1.2 

1.5 

1.7 

2.0 

2.2 

2.453 

-22.0 

-29 

0.3 

0.5 

0.8 

1.1 

1.4 

1.6 

1.9 

2.2 

2.2 

2.700 

-20.2 

-28 

0.3 

0.6 

0.9 

1.2 

1.5 

1.8 

2.1 

2.4 

2.7 

2.967 

-18.4 

-27 

0.3 

0.7 

1.0 

1.3 

1.6 

2.0 

2.3 

2.6 

2.9 

3.261 

-16.6 

-26 

0.4 

0.7 

1.1 

1.4 

1.8 

2.1 

2.5 

2.9 

3.2 

3.580 

-14.8 

-25 

0.4 

0.8 

1.2 

1.6 

2.0 

2.4 

2.7 

3.1 

3.5 

3.925 

-13.0 

-24 

0.4 

0.9 

1.3 

1.7 

2.2 

2.6 

3.0 

3.4 

3.9 

4.301 

-11.2 

-23 

0.5 

0.9 

1.4 

1.9 

2.4 

2.8 

3.3 

3.8 

4.2 

4.708 

- 9.4 

-22 

0.5 

1.0 

1.5 

2.1 

2.6 

3.1 

3.6 

4.1 

4.6 

5.155 

- 7.6 

-21 

0.6 

1.1 

1.7 

2.3 

2.8 

3.4 

3.9 

4.5 

5.1 

5.637 

- 5.8 

-20 

0.6 

1.2 

1.8 

2.5 

3.1 

3.7 

4.3 

4.9 

5.5 

6.130 

- 4.0 

-19 

0.7 

1.3 

2.0 

2.7 

3.4 

4.0 

4.7 

5.4 

6.1 

6.724 

- 2.2 

-18 

0.7 

1.5 

2.2 

2.9 

3.7 

4.4 

5.1 

5.8 

6.6 

7.309 

- .4 

-17 

0.8 

1.6 

2.4 

3.2 

4.0 

4.8 

5.6 

6.4 

7.2 

7.999 

+ 1.4 

-16 

0.9 

1.7 

2.6 

3.5 

4.3 

5.2 

6.1 

6.9 

7.8 

8.678 

+ 3.2 

-15 

0.9 

1.9 

2.8 

3.8 

4.7 

5.7 

6.6 

7.6 

8.5 

9.461 

+ 5.0 

-14 

1.0 

2.1 

3.1 

4.1 

5.1 

6.2 

7.2 

8.2 

9.3 

10.287 

+ 6.8 

-13 

1.1 

2.2 

3.3 

4.5 

5.6 

6.7 

7.8 

8.9 

10.0 

11.157 

+ 8.6 

-12 

1.2 

2.4 

3.6 

4.8 

6.1 

7.3 

8.5 

9.7 

10.9 

12.124 

+ 10.4 

-11 

1.3 

2.6 

4.0 

5.3 

6.6 

7.9 

9.2 

10.5 

11.9 

13.185 

+ 12.2 

-10 

1.4 

2.9 

4.3 

5.7 

7.1 

8.6 

10.0 

11.4 

12.9 

14.284 

+ 14.0 

- 9 

1.5 

3.1 

4.6 

6.2 

7.7 

9.3 

10.8 

12.4 

13.9 

15.472 

+ 15.8 

- 8 

1.7 

3.4 

5.0 

6.7 

8.4 

10.1 

11.7 

13.4 

15.1 

16.754 

+ 17.6 

- 7 

1.8 

3.6 

5.4 

7.2 

9.1 

10.9 

12.7 

14.5 

16.3 

18.117 

+ 19.4 

- 6 

2.0 

3.9 

5.9 

7.8 

9.8 

11.7 

13.7 

15.7 

17.6 

19.568 

+21.2 

- 5 

2.1 

4.2 

6.3 

8.5 

10.6 

12.7 

14.8 

16.9 

19.0 

21.156 

+23.0 

- 4 

2.3 

4.6 

6.9 

9.1 

11.4 

13.7 

16.0 

18.3 

20.6 

22.871 

+24.8 

- 3 

2.5 

4.9 

7.4 

9.9 

12.3 

14.8 

17.3 

19.7 

22.2 

24.670 

+26.6 

- 2 

2.7 

5.3 

8.0 

10.6 

13.3 

16.0 

18.6 

21.3 

23.9 

26.589 

+28.4 

- 1 

2.9 

5.7 

8.6 

11.5 

14.3 

17.2 

20.1 

22.9 

25.8 

28.685 

+30.2 

± 0 

3.1 

6.2 

9.3 

12.4 

15.5 

18.5 

21.6 

24.7 

27.8 

30.911 

+32.0 

1 

3.3 

6.6 

9.9 

13.2 

16.5 

19.8 

23.0 

26.3 

29.6 

32.919 

+33.8 

2 

3.5 

7.0 

10.5 

14.1 

17.6 

21.1 

24.6 

28.1 

31.6 

35.139 

+35.6 

3 

3.8 

7.5 

11.3 

15.0 

18.8 

22.5 

26.3 

30.0 

33.8 

37.509 

+37.4 

4 

4.0 

8.0 

12.0 

16.0 

20.0 

24.0 

28.0 

32.0 

35.9 

39.939 

+39.2 

5 

4.3 

8.5 

12.8 

17.0 

21.3 

25.5 

29.8 

34.0 

38.3 

42.533 

+41.0 

6 

4.5 

9.1 

13.6 

18.1 

22.6 

27.2 

31.7 

36.2 

40.8 

45.280 

+42.8 

7 

4.8 

9.6 

14.5 

19.3 

24.1 

28.9 

33.7 

38.5 

43.3 

48.175 

+44.6 

8 

5.1 

10.2 

15.4 

20.5 

25.6 

30.7 

35.9 

41.0 

46.1 

51.215 

+46.4 

9 

5.4 

10.9 

16.3 

21.8 

27.2 

32.6 

38.1 

43.5 

49.0 

54.394 

+48.2 

10 

5.8 

11.6 

17.3 

23.1 

. 28.9 

34.7 

40.5 

46.2 

52.0 

57.793 

+50.0 

11 

6.1 

12.3 

18.4 

24.5 

30.6 

36.8 

42.9 

49.0 

55.1 

61.270 

+51.8 

12 

6.5 

13.0 

19.5 

26.0 

32.5 

39.1 

45.6 

52.1 

58.6 

65.094 

+53.6 

13 

6.9 

13.8 

20.7 

27.6 

34.5 

41.4 

48.3 

55.2 

62.1 

69.010 

+55.4 

14 

7.3 

14.6 

22.0 

29.3 

36.6 

43.9 

51.2 

58.5 

65.9 

73.169 

+57.2 

15 

7.8 

15.5 

23.3 

31.0 

38.8 

46.5 

54.3 

62.0 

69.8 

77.505 

+59.0 

16 

8.2 

16.4 

24.6 

32.8 

41.0 

49.2 

57.4 

65.6 

73.9 

82.060 

+60.8 

17 

8.7 

17.4 

26.0 

34.7 

43.4 

52.1 

60.8 

69.5 

78.1 

86.813 

+62.6 

18 

9.2 

18.4 

27.6 

36.7 

45.9 

55.1 

64.3 

73.5 

82.7 

91.866 

+64.4 

19 

9.7 

19.4 

29.1 

38.9 

48.6 

58.3 

68.0 

77.7 

87.4 

97.127 

+66.2 

20 

10.3 

20.5 

30.8 

41.1 

51.4 

61.6 

71.9 

82.2 

92.4 

102.71 

+68.0 

21 

10.8 

21.7 

32.5 

43.4 

54.2 

65.1 

75.9 

86.8 

97.6 

108.46 

+69.8 

22 

11.5 

22.9 

34.4 

45.8 

57.3 

68.7 

80.2 

91.6 

103.1 

114.56 

+71.6 

23 

12.1 

24.2 

36.3 

48.3 

60.4 

72.5 

84.6 

96.7 

108.8 

120.87 

+73.4 

24 

12.8 

25.5 

38.3 

51.0 

63.8 

76.5 

89.3 

102.0 

114.8 

127.53 

+ 75.2 

25 

13.4 

26.9 

40.3 

53.8 

67.2 

80.7 

94.1 

107.6 

121.0 

134.44 

+ 77.0 

26 

14.2 

28.3 

42.5 

56.7 

70.9 

85.0 

99.2 

113.4 

127.6 

141.74 

+78.8 

27 

14.9 

29.9 

44.8 

59.8 

74.7 

89.6 

104.6 

119.5 

134.5 

149.39 

+80.6 

28 

15.7 

31.5 

47.2 

62.9 

78.7 

94.4 

110.1 

125.9 

141.6 

157.34 

+82.4 

29 

16.6 

33.1 

49.7 

66.2 

82.8 

99.4 

115.9 

132.5 

149.1 

165.62 

+84.2 

30 

17.4 

34.9 

52.3 

69.7 

87.1 

104.6 

122.0 

139.4 

156.8 

174.27 

+86.0 

31 

18.3 

36.7 

55.0 

73.3 

91.7 

110.0 

128.3 

146.7 

165.0 

183.32 

+87.8 

32 

19.3 

38.5 

57.8 

77.1 

96.4 

115.6 

134.9 

154.2 

173.5 

192.74 

+89.6 

33 

20.3 

40.5 

60.8 

81.0 

101.3 

121.5 

141.8 

162.0 

182.3 

202.56 

+91.4 

34 

21.3 

42.6 

63.9 

85.1 

106.4 

127.7 

149.0 

170.3 

191.6 

212.86 

+93.2 

35 

22.4 

44.7 

67.1 

89.4 

111.8 

134.1 

156.5 

178.8 

201.2 

223.50 

+95.0 

36 

23.5 

46.9 

70.4 

93.9 

117.3 

140.8 

164.2 

187.7 

211.2 

234.63 

+96.8 

37 

24.6 

49.2 

73.9 

98.5 

123.1 

147.7 

172.3 

197.0 

221.6 

246.20 

+98.6 

38 

25.8 

51.6 

77.5 

103.3 

129.1 

154.9 

180.8 

206.6 

232.4 

258.23 

+ 100.4 

39 

27.1 

54.2 

81.2 

108.3 

135.4 

162.5 

189.6 

216.6 

243.7 

270.80 

+ 102.2 

40 

28.4 

56.8 

85.2 

113.6 

142.0 

170.4 

198.8 

227.2 

255.5 

283.94 

+ 104.0 



COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


83 


Table 6. / for t from -30 C (-22 F) to 40 C (104 F). 


t c 

/ 

t F 

t ( 


/ 

1 F 

t C 

: / 

1 F 

-30 

6.390 

-22.0 

— 

6 

5.289 

+21.2 

+ 18 

4.449 

+64.4 

-29 

6.338 

-20.2 

— 

5 

5.250 

+ 23.0 

+ 19 

4.419 

+66.2 

-28 

6.286 

-18.4 

— 

4 

5.210 

+ 24.8 

+20 

4.389 

+68.0 

-27 

6.233 

-16.6 

— 

3 

5.172 

+ 26.6 

+21 

4.359 

+69.8 

-26 

6.183 

-14.8 

— 

2 

5.133 

+28.4 

+22 

4.330 

+71.6 

-25 

6.134 

-13.0 

— 

1 

5.095 

+ 30.2 

+23 

4.300 

+73.4 

-24 

6.084 

-11.2 


0 

5.059 

+ 32.0 

+24 

4.271 

+75.2 

-23 

6.036 

- 9.4 

+ 

1 

5.021 

+33.8 

+25 

4.241 

+77.0 

-22 

5.988 

- 7.6 

+ 

2 

4.984 

+35.6 

+26 

4.213 

+78.8 

-21 

5.940 

- 5.8 

+ 

3 

4.948 

+37.4 

+27 

4.186 

+80.6 

-20 

5.894 

- 4.0 

+ 

4 

4.913 

+39.2 

+28 

4.158 

+82.4 

-19 

5.847 

— 2.2 

+ 

5 

4.878 

+41.0 

+29 

4.130 

+84.2 

-18 

5.801 

- .4 

+ 

6 

4.843 

+42.8 

+30 

4.102 

+86.0 

-17 

5.755 

+ 1.4 

+ 

7 

4.808 

+44.6 

+31 

4.076 

+87.8 

-16 

5.710 

+ 3.2 

+ 

8 

4.773 

+46.4 

+32 

4.049 

+89.6 

-15 

5.666 

+ 5,0 

+ 

9 

4.738 

+48.2 

+33 

4.022 

+91.4 

-14 

5.622 

+ 6.8 

+ 10 

4.706 

+50.0 

+34 

3.997 

+93.2 

-13 

5.579 

+ 8.6 

+ 11 

4.666 

+51.8 

+35 

3.970 

+95.0 

-12 

5.537 

+ 10.4 

+ 12 

4.640 

+53.6 

+36 

3.944 

+96.8 

-11 

5.494 

+ 12.2 

+ 13 

4.607 

+55.4 

+37 

3.918 

+98.6 

-10 

5.452 

+ 14.0 

+ 14 

4.576 

+57.2 

+38 

3.893 

+ 100.4 

- 9 

5.410 

+ 15.8 

+ 15 

4.543 

+59.0 

+39 

3.868 

+ 102.2 

- 8 

5.370 

+ 17.6 

+ 16 

4.511 

+60.8 

+40 

3.844 

+ 104.0 

- 7 

5.329 

+ 19.4 

+ 17 

4.480 

+62.6 





Table 7. for h from 10 m (32.8 ft) to 2,000 m (6,562 ft). 


h(m) 

1 M, 

h{h) 

him) M, 

/i(ft) 

him) 

Me 

/i(ft) 

10 

1.6 

32.8 

280 

44.0 

918.6 

625 

98.1 

2,051.0 

20 

3.1 

65.6 

290 

45.5 

951.4 

650 

102.1 

2,133.0 

30 

4.7 

98.4 

300 

47.1 

984.3 

675 

106.0 

2,215.0 

40 

6.3 

131.2 

310 

48.7 

1,017.0 

700 

109.9 

2,297.0 

50 

7.9 

164.0 

320 

50.2 

1,050.0 

725 

113.8 

2,379.0 

60 

9.4 

196.9 

330 

51.8 

1,083.0 

750 

117.8 

2,461.0 

70 

11.0 

229.7 

340 

53.4 

1,115.0 

775 

121.7 

2,543.0 

80 

12.6 

262.5 

350 

55.0 

1,148.0 

800 

125.6 

2,625.0 

90 

14.1 

295.3 

360 

56.5 

1,181.0 

825 

129.5 

2,707.0 

100 

15.7 

328.1 

370 

58.1 

1,214.0 

850 

133.5 

2,789.0 

110 

17.3 

360.9 

380 

59.7 

1,247.0 

875 

137.4 

2,871.0 

120 

18.8 

393.7 

390 

61.2 

1,280.0 

900 

141.3 

2,953.0 

130 

20.4 

426.5 

400 

62.8 

1,312.0 

925 

145.2 

3,035.0 

140 

22.0 

459.3 

410 

64.4 

1,345.0 

950 

149.2 

3,117.0 

150 

23.6 

492.1 

420 

65.9 

1,378.0 

975 

153.1 

3,199.0 

160 

25.1 

524.9 

430 

67.5 

1,411.0 

1,000 

157.0 

3,280.0 

170 

26.7 

557.7 

440 

69.1 

1,444.0 

1,100 

172.7 

3,609.0 

180 

28.3 

590.6 

450 

70.7 

1,476.0 

1,200 

188.4 

3,937.0 

190 

29.8 

623.4 

460 

72.2 

1,509.0 

1,300 

204.1 

4,265.0 

200 

31.4 

656.2 

470 

73.8 

1,542.0 

1,400 

219.8 

4,593.0 

210 

33.0 

689.0 

480 

75.4 

1,575.0 

1,500 

235.5 

4,921.0 

220 

34.5 

721.8 

490 

76.9 

1,608.0 

1,600 

251.2 

5,249.0 

230 

36.1 

754.6 

500 

78.5 

1,640.0 

1,700 

266.9 

5,577.0 

240 

37.7 

787.4 

525 

82.4 

1,722.0 

1,800 

282.6 

5,906.0 

250 

39.3 

820.2 

550 

86.4 

1,804.0 

1,900 

298.3 

6,234.0 

260 

40.8 

853.0 

575 

90.3 

1,886.0 

2,000 

314.0 

6,562.0 

270 

42.4 

885.8 

600 

94.2 

1,969.0 





84 


METEOROLOGY— THEORY 


\ 

<c\ 

w 

0 

Table 84 . F { t , w ) for 1 from — 

1 2 3 4 5 

30 C (- 

6 

22 F ) to 40 C (104 F ); w from 0 

7 8 9 10 

to 12 . 

11 

w 

12 

/+F 

-30 

325.1 

335.1 












- 22.0 

-29 

323.8 

333.9 












- 20.2 

-28 

322.4 

332.4 












- 18.4 

-27 

321.1 

331.0 












- 16.6 

-26 

319.8 

329.7 












- 14.8 

-25 

318.5 

328.3 












- 13.0 

-24 

317.3 

327.0 












- 11.2 

-23 

316.0 

325.6 












- 9.4 

-22 

314.7 

324.3 












- 7.6 

-21 

313.5 

323.0 












- 5.8 

-20 

312.3 

321.7 












- 4.0 

-19 

311.0 

320.3 












- 2.2 

-18 

309.8 

319.1 












- 0.4 

-17 

308.6 

317.8 












+ 1.4 

-16 

307.4 

316.5 












+ 3.2 

-15 

306.2 

315.9 

324.9 











+ 5.0 

-14 

305.0 

314.0 

322.8 











+ 6.8 

-13 

303.8 

312.7 

' 321.6 











+ 8.6 

-12 

302.7 

311.6 

320.4 











+ 10.4 

-11 

301.5 

310.3 

319.0 











+ 12.2 

-10 

300.4 

309.1 

317.8 











+ 14.0 

- 9 

299.2 

307.9 

316.5 











+ 15.8 

- 8 

298.1 

306.7 

315.3 











+ 17.6 

- 7 

297.0 

305.5 

314.0 

322.5 










+ 19.4 

- 6 

295.9 

304.4 

312.8 

321.2 










+ 21.2 

- 5 

294.8 

303.2 

311.6 

319.9 










+ 23.0 

- 4 

293.7 

302.0 

310.4 

318.7 










+ 24.8 

- 3 

292.6 

300.9 

309.1 

317.4 










+ 26.6 

- 2 

291.5 

299.7 

307.9 

316.1 

324.2 









+ 28.4 

- 1 

290.4 

298.6 

306.7 

314.8 

322.9 









+ 30.2 

± 0 

289.4 

297.5 

305.6 

313.6 

321.7 









+ 32.0 

+ 1 

288.3 

296.4 

304.4 

312.4 

320.4 

328.3 








+ 33.8 

+ 2 

287.3 

295.3 

303.3 

311.2 

319.1 

327.0 








+ 35.6 

+ 3 

286.2 

294.1 

302.0 

309.9 

317.8 

325.6 








+ 37.4 

+ 4 

285.2 

293.1 

300.9 

308.8 

316.6 

324.4 

332.0 







+ 39.2 

+ 5 

284.2 

292.0 

299.8 

307.6 

315.4 

323.1 

330.7 







+ 41.0 

+ 6 

283.2 

291.0 

298.7 

306.4 

314.1 

321.7 

329.4 







+ 42.8 

+ 7 

282.1 

289.8 

297.5 

305.2 

312.8 

320.3 

327.9 

335.5 






+ 44.6 

+ 8 

281.1 

288.8 

296.4 

304.0 

311.5 

319.1 

326.6 

334.1 






+ 46.4 

+ 9 

280.1 

287.7 

295.3 

302.8 

310.3 

317.8 

325.3 

332.8 

340.2 





+ 48.2 

+ 10 

279.2 

286.8 

294.3 

301.8 

309.2 

316.7 

324.1 

331.6 

338.8 





+ 50.0 

+ 11 

278.2 

285.7 

293.2 

300.5 

307.9 

315.3 

322.7 

330.1 

337.3 

344.6 




+ 51.8 

+ 12 

277.2 

284.7 

292.1 

299.4 

306.8 

314.1 

321.5 

328.8 

336.0 

343.3 

350.5 



+ 53.6 

+ 13 

276.2 

283.6 

291.0 

298.2 

305.6 

312.9 

320.2 

327.4 

334.0 

341.8 

349.0 



+ 55.4 

+ 14 

275.3 

282.7 

290.0 

297.2 

304.5 

311.7 

319.0 

326.2 

333.3 

340.5 

347.6 

354.7 


+ 57.2 

+ 15 

274.3 

281.6 

288.9 

296.0 

302.3 

310.5 

317.7 

324.9 

331.9 

339.0 

346.1 

353.1 

360.2 

+ 59.0 

+ 16 

273.4 

280.7 

287.9 

295.0 

302.2 

309.3 

316.4 

323.5 

330.6 

337.6 

344.7 

351.7 

358.6 

+ 60.8 

+ 17 

272.4 

279.6 

286.8 

293.8 

301.0 

308.1 

315.1 

322.2 

329.2 

336.1 

343.2 

350.2 

357.0 

+ 62.6 

+ 18 

271.5 

278.7 

285.7 

292.8 

299.9 

307.0 

313.9 

320.9 

327.9 

334.8 

341.8 

348.7 

355.6 

+ 64.4 

+ 19 

270.5 

277.6 

284.6 

291.7 

298.7 

305.5 

312.6 

319.6 

326.6 

333.4 

340.3 

347.1 

354.0 

+ 66.2 

+20 

269.6 

276.7 

283.6 

290.6 

297.6 

304.5 

311.5 

318.4 

325.2 

332.1 

339.0 

345.7 

352.6 

+ 68.0 

+21 

268.7 

275.7 

282.6 

289.6 

296.5 

303.4 

310.3 

317.2 

323.9 

330.8 

337.5 

344.3 

351.1 

+ 69.8 

+22 

267.8 

274.8 

281.6 

288.5 

295.5 

302.2 

309.1 

315.9 

322.7 

329.5 

336.2 

342.9 

349.7 

+ 71.6 

+23 

266.9 

273.8 

280.6 

287.5 

294.4 

301.1 

307.9 

314.7 

321.4 

328.2 

334.8 

341.5 

348.1 

+ 73.4 

+24 

266.0 

272.9 

279.6 

286.5 

293.3 

300.0 

306.8 

313.4 

320.2 

326.9 

333.5 

340.1 

346.7 

+ 75.2 

+25 

265.1 

271.9 

278.6 

285.4 

292.2 

298.9 

305.6 

312.2 

318.9 

325.4 

332.1 

338.7 

345.2 

+ 77.0 

+26 

264.2 

271.0 

277.7 

284.4 

291.0 

297.7 

304.4 

311.0 

317.6 

324.2 

330.8 

337.3 

343.8 

+ 78.8 

+27 

263.3 

270.0 

276.7 

283.4 

290.0 

296.6 

303.3 

309.8 

316.4 

322.9 

329.5 

335.9 

342.4 

+ 80.6 

+28 

262.5 

269.2 

275.8 

282.4 

289.0 

295.6 

302.2 

308.7 

315.3 

321.7 

328.2 

334.6 

341.1 

+ 82.4 

+29 

261.6 

268.3 

274.8 

281.4 

287.9 

294.5 

300.9 

307.5 

314.0 

320.4 

326.9 

333.3 

339.7 

+ 84.2 

+30 

260.7 

267.3 

273.8 

280.4 

286.8 

293.4 

299.8 

306.3 

312.7 

319.1 

325.5 

331.9 

338.2 

+ 86.0 

+31 

259.9 

266.5 

272.9 

279.5 

285.9 

292.4 

298.7 

305.2 

311.5 

318.0 

324.3 

330.6 

336.9 

+ 87.8 

+32 

259.0 

265.5 

271.9 

278.4 

284.8 

291.3 

297.6 

304.0 

310.3 

316.7 

323.0 

329.3 

335.5 

+ 89.6 

+33 

258.2 

264.7 

271.1 

277.5 

283.8 

290.3 

296.5 

302.9 

309.2 

315.5 

321.7 

328.0 

334.2 

+ 91.4 

+34 

257.3 

263.8 

270.1 

276.5 

282.8 

289.2 

295.4 

301.7 

308.0 

314.2 

320.4 

326.7 

332.8 

+ 93.2 

+35 

256.5 

262.9 

269.2 

275.6 

281.8 

288.1 

294.4 

300.7 

306.8 

313.0 

319.2 

325.3 

331.6 

+ 95.0 

+36 

255.7 

262.1 

268.3 

274.6 

280.9 

287.2 

293.3 

299.5 

305.7 

311.8 

318.0 

324.1 

330.3 

+ 96.8 

+37 

254.8 

261.1 

267.3 

273.5 

279.8 

286.0 

292.2 

298.3 

304.5 

310.6 

316.7 

322.8 

328.8 

+ 98.6 

+ 38 

254.0 

260.3 

266.5 

272.6 

278.8 

285.0 

291.1 

297.2 

303.4 

309.4 

315.5 

321.5 

327.5 

+ 100.4 

+39 

253.2 

259.4 

265.6 

271.7 

277.9 

284.0 

290.1 

296.2 

302.3 

308.3 

314.3 

320.3 

326.3 

+ 102.2 

+40 

252.4 

258.5 

264.7 

270.8 

276.9 

283.0 

289.1 

295.1 

301.2 

307.1 

313.1 

319.1 

325.1 

+ 104.0 



COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


85 


Table 8B. F{t, w) for I from 15 C (59 F) to 40 C (104 F); w from 12 to 24. 


\ 

tc\ 

w 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

w 

24 

/ F 

15 

360.2 













59.0 

16 

358.6 













60.8 

17 

357.0 

364.0 












62.6 

18 

355.6 

362.5 

369.2 











64.4 

19 

354.0 

360.9 

367.6 











66.2 

20 

352.6 

359.3 

366.1 

372.8 










68.0 

21 

351.1 

357.8 

364.5 

371.1 

377.9 









69.8 

22 

349.7 

356.3 

363.0 

369.6 

376.2 

382.8 








71.6 

23 

348.1 

354.8 

361.5 

368.0 

374.6 

381.1 

387.7 







73.4 

24 

346.7 

353.3 

359.8 

366.4 

372.9 

379.5 

385.9 

392.4 






75.2 

25 

345.2 

351.8 

358.3 

364.8 

371.3 

377.7 

384.2 

390.6 

397.0 

403.4 




77.0 

26 

343.8 

350.3 

356.8 

363.2 

369.7 

376.1 

382.5 

388.9 

295.3 

401.6 

407.9 



78.8 

27 

342.4 

348.8 

355.3 

361.7 

368.1 

374.5 

380.9 

387.2 

393.5 

399.8 

406.0 

412.3 

418.5 

80.6 

28 

341.1 

347.5 

353.9 

360.2 

366.7 

372.9 

379.2 

385.6 

391.8 

398.1 

404.3 

410.5 

416.7 

82.4 

29 

339.7 

346.0 

352.3 

358.7 

365.0 

371.3 

377.6 

383.9 

390.0 

396.2 

402.5 

408.6 

414.7 

84.2 

30 

338.2 

344.6 

350.8 

357.2 

363.4 

369.6 

375.9 

382.1 

388.3 

394.5 

400.6 

406.8 

412.8 

86.0 

31 

336.9 

343.2 

349.5 

355.8 

362.0 

368.1 

374.4 

380.5 

386.7 

392.8 

398.9 

405.0 

411.1 

87.8 

32 

335.5 

341.8 

348.0 

354.1 

360.4 

366.5 

372.7 

378.8 

384.9 

391.1 

397.1 

403.1 

409.2 

89.6 

33 

334.2 

340.4 

346.6 

352.7 

359.0 

365.0 

371.1 

377.3 

383.3 

389.3 

395.4 

401.4 

407.3 

91.4 

34 

332.8 

339.0 

345.2 

351.3 

357.4 

363.5 

369.5 

375.6 

381.6 

387.6 

393.7 

399.6 

405.5 

93.2 

35 

331.6 

337.6 

343.8 

349.8 

355.9 

362.0 

368.0 

374.0 

380.0 

386.0 

391.9 

397.9 

403.8 

95.0 

36 

330.3 

336.3 

342.4 

348.5 

354.4 

360.4 

366.5 

372.4 

378.3 

384.3 

390.2 

396.1 

402.0 

96.8 

37 

328.8 

334.9 

340.9 

346.9 

352.9 

358.8 

364.8 

370.8 

376.6 

382.5 

388.5 

394.3 

400.1 

98.6 

38 

327.5 

333.6 

339.6 

345.5 

351.5 

357.4 

363.3 

369.3 

375.1 

380.9 

386.8 

392.6 

398.4 

100.4 

39 

326.3 

332.3 

338.2 

344.1 

350.1 

355.9 

361.8 

367.9 

373.5 

379.3 

385.1 

390.9 

396.7 

102.2 

40 

325.1 

330.9 

336.9 

342.8 

348.6 

354.5 

360.3 

366.5 

371.9 

377.8 

383.5 

389.2 

394.9 

104.0 




Table 8C. F{t, w) for t from 27 C (80.6 F) to 40 C (104 F); lo from 24 to 36. 



\ 

tc\ 

w 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

10 y' 

y IF 

27 

418.5 













80.6 

28 

416.7 

422.9 












82.4 

29 

414.7 

421.0 

427.1 











84.2 

30 

412.8 

418.9 

425.2 

431.1 

437.1 









86.0 

31 

411.1 

417.1 

423.2 

429.2 

435.2 

441.2 

447.2 







87.8 

32 

409.2 

415.2 

421.2 

427.2 

433.2 

439.2 

445.0 

451.0 

456.8 

462.6 




89.6 

33 

407.3 

413.4 

419.3 

425.3 

431.1 

437.2 

443.0 

448.8 

454.6 

460.5 

466.4 

472.1 


91.4 

34 

405.5 

411.5 

417.4 

423.3 

429.2 

435.1 

440.9 

446.7 

452.5 

458.4 

464.1 

469.9 

475.6 

93.2 

35 

403.8 

409.6 

415.6 

421.4 

427.2 

433.1 

439.9 

444.7 

450.4 

456.2 

461.9 

467.7 

473.4 

95.0 

36 

402.0 

407.9 

413.7 

419.5 

425.4 

431.1 

436.9 

442.6 

448.3 

454.1 

459.8 

465.5 

471.1 

96.8 

37 

400.1 

405.9 

411.8 

417.6 

423.3 

429.0 

434.8 

440.5 

446.2 

451.9 

457.5 

463.1 

468.9 

98.6 

38 

398.4 

404.1 

410.0 

415.7 

421.4 

427.1 

432.9 

438.5 

444.2 

449.8 

455.4 

461.0 

466.7 

100.4 

39 

396.7 

402.4 

408.1 

413.9 

419.6 

425.3 

430.9 

436.5 

442.1 

447.8 

453.4 

458.9 

464.5 

102.2 

40 

394.9 

400.7 

406.4 

412.1 

417.7 

423.4 

429.0 

434.6 

440.2 

445.7 

451.3 

456.8 

462.4 

104.0 


Table 8D. F{t, w) for I from 34 C (93.2 F) to 40 C (104 F); w from 30 to 45. 


w 


w 


iC\ 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

/ tF 

34 

475.6 










93.20 

35 

473.4 

479.1 









95.00 

36 

471.1 

476.8 

482.4 

488.1 

493.7 






96.80 

37 

468.9 

474.5 

480.1 

485.6 

491.2 

496.7 

502.2 

507.7 



98.60 

38 

466.7 

472.3 

477.8 

483.3 

488.9 

494.4 

499.8 

505.3 

510.8 


100.40 

39 

464.5 

470.0 

475.5 

481.0 

486.6 

492.1 

497.5 

502.9 

508.4 

513.8 

102.20 

40 

462.4 

467.9 

473.4 

478.9 

484.3 

489.8 

495.2 

500.6 

506.0 

511.4 

104.00 


86 


METEOROLOGY— THEORY 


\ 

h ( m )^ 

50 

100 

150 

200 

250 

300 

350 

400 

450 

500 

600 

700 

800 

900 

1,000 

1,500 

2,000 




t = 


Table 9 . p/po for h from 50 m (164 ft) to 2,000 m ( 6,562 ft) and t * from —30 C ( — 22 F ) to 40 C (104 F ). 

/ 

/h (ft) 

164.0 

328.1 

492.1 

656.2 

820.2 

984.3 

1 . 148.0 

1 . 312.0 

1 . 476.0 

1 . 640.0 

1 . 969.0 

2 . 297.0 

2 . 625.0 

2 . 953.0 

3 . 281.0 

4 . 921.0 

6 . 562.0 


IC 

-30 -25 -20 -15 -10 - 5 ±0 +5 +10 +15 +20 +25 +30 +35 +40 


0.9930 0.9931 0.9933 0.9934 0.9935 0.9936 0.9938 0.9939 0.9940 0.9941 0.9942 0.9943 0.9944 0.9945 0.9946 

0.9860 0.9863 0.9866 0.9869 0.9871 0.9874 0.9876 0.9878 0.9880 0.9882 0.9884 0.9886 0.9888 0.9890 0.9892 

0.9791 0.9795 0.9799 0.9802 0.9807 0.9810 0.9814 0.9817 0.9821 0.9823 0.9827 0.9829 0.9832 0.9835 0.9837 

0.9723 0.9727 0.9734 0.9738 0.9744 0.9748 0.9753 0.9757 0.9761 0.9766 0.9770 0.9774 0.9777 0.9780 0.9784 

0.9655 0.9662 0.9668 0.9674 0.9681 0.9686 0.9692 0.9698 0.9703 0.9707 0.9713 0.9717 0.9722 0.9727 0.9730 

0.9587 0.9595 0.9603 0.9610 0.9618 0.9625 0.9632 0.9637 0.9644 0.9650 0.9656 0.9662 0.9667 0.9672 0.9678 

0.9519 0.9529 0.9538 0.9547 0.9556 0.9564 0.9572 0.9579 0.9586 0.9593 0.9600 0.9607 0.9613 0.9619 0.9625 

0.9453 0.9464 0.9474 0.9484 0.9494 0.9503 0.9512 0.9519 0.9529 0.9537 0.9544 0.9551 0.9559 0.9566 0.9572 

0.9387 0.9399 0.9410 0.9421 0.9432 0.9442 0.9452 0.9462 0.9471 0.9480 0.9489 0.9497 0.9505 0.9513 0.9520 

0.9321 0.9334 0.9347 0.9359 0.9371 0.9383 0.9394 0.9404 0.9414 0.9424 0.9434 0.9443 0.9452 0.9460 0.9469 

0.9191 0.9206 0.9222 0.9236 0.9250 0.9263 0.9277 0.9289 0.9301 0.9313 0.9324 0.9335 0.9346 0.9355 0.9366 

0.9063 0.9081 0.9098 0.9115 0.9131 0.9146 0.9161 0.9176 0.9190 0.9203 0.9216 0.9229 0.9241 0.9253 0.9264 

0.8936 0.8957 0.8976 0.8995 0.9013 0.9030 0.9047 0.9063 0.9079 0.9095 0.9109 0.9124 0.9138 0.9151 0.9164 

0.8812 0.8834 0.8856 0.8876 0.8897 0.8916 0.8935 0.8953 0.8971 0.8987 0.9004 0.9019 0.9035 0.9050 0.9064 

0.8688 0.8712 0.8737 0.8760 0.8782 0.8803 0.8824 0.8843 0.8863 0.8881 0.8899 0.8917 0.8934 0.8950 0.8966 

0.8099 0.8133 0.8166 0.8198 0.8230 0.8260 0.8289 0.8317 0.8344 0.8370 0.8395 0.8420 0.8444 0.8467 0.8490 

0.7549 0.7592 0.7633 0.7674 0.7712 0.7749 0.7786 0.7821 0.7855 0.7888 0.7920 0.7951 0.7981 0.8011 0.8039 


- 22.0 - 13.0 - 4.0 + 5.0 + 14.0 + 23.0 + 32.0 + 41.0 + 50.0 + 59.0 + 68.0 + 77.0 + 86.0 + 95.0 + 104.0 

temperature averaged from the ground to the height h . ^ F \ 


(ft) 


Table lOA . u for h from 10 m ( 32.8 ft ) to 150 m ( 492.1 ft ); F from 250 to 370 . Values to be subtracted from F to 
obtain Fp = (n — 1 ) 10 ®. 


F / 


h ( m )\ 

250 

260 

270 

280 

290 

300 

310 

320 

330 

340 

350 

360 

370 

/h ( ft ) 

10 

0.3 

0.3 

0.3 

0.3 

0.3 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

32.8 

20 

0.6 

0.7 

0.7 

0.7 

0.7 

0.8 

0.8 

0.8 

0.8 

0.9 

0.9 

0.9 

0.9 

65.6 

30 

0.9 

1.0 

1.0 

1.0 

1.1 

1.1 

1.1 

1.2 

1.2 

1.3 

1.3 

1.3 

1.4 

98.4 

40 

1.3 

1.3 

1.4 

1.4 

1.5 

1.5 

1.6 

1.6 

1.7 

1.7 

1.8 

1.8 

1.9 

131.2 

50 

1.6 

1.6 

1.7 

1.7 

1.8 

1.9 

1.9 

2.0 

2.0 

2.1 

2.2 

2.2 

2.3 

164.0 

60 

1.9 

1.9 

2.0 

2.1 

2.1 

2.2 

2.3 

2.4 

2.4 

2.5 

2.6 

2.7 

2.7 

196.9 

70 

2.2 

2.3 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

229.7 

80 

2.5 

2.6 

2.7 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

262.5 

90 

2.8 

2.9 

3.0 

3.1 

3.2 

3.4 

3.5 

3.6 

3.7 

3.8 

3.9 

4.0 

4.1 

295.3 

100 

3.1 

3.2 

3.3 

3.5 

3.6 

3.7 

3.8 

4.0 

4.1 

4.2 

4.3 

4.5 

4.6 

328.1 

110 

3.4 

3.5 

3.7 

3.8 

3.9 

4.1 

4.2 

4.4 

4.5 

4.6 

4.8 

4.9 

5.0 

360.9 

120 

3.7 

3.9 

4.0 

4.2 

4.3 

4.5 

4.6 

4.8 

4.9 

5.1 

5.2 

5.4 

5.5 

393.7 

130 

4.0 

4.2 

4.3 

4.5 

4.7 

4.8 

5.0 

5.2 

5.3 

5.5 

5.6 

5.8 

6.0 

426.5 

140 

4.4 

4.5 

4.7 

4.9 

5.0 

5.2 

5.4 

5.6 

5.7 

5.9 

6.1 

6.3 

6.4 

459.3 

150 

4.7 

4.8 

5.0 

5.2 

5.4 

5.6 

5.8 

6.0 

6.1 

6.3 

6.5 

6.7 

6.9 

492.1 


Table lOB . u for h from 10 m ( 32.8 ft) to 150 m ( 492.1 ft); F from 370 to 500 . Values to be subtracted from F * to 
obtain Fp = (n — 1) 10®. 


/^( m )\ 

370 

380 

390 

400 

410 

420 

430 

440 

450 

460 

470 

480 

490 

500 

/ h { h ) 

10 

0.4 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.6 

0.6 

0.6 

0.6 

0.6 

32.8 

20 

0.9 

1.0 

1.0 

1.0 

1.0 

1.1 

1.1 

1.1 

1.1 

1.2 

1.2 

1.2 

1.2 

1.3 

65.6 

30 

1.4 

1.4 

1.4 

1.5 

1.5 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.9 

98.4 

40 

1.9 

1.9 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

131.2 

50 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3.0 

3.0 

3.1 

164.0 

60 

2.7 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

3.3 

3.3 

3.4 

3.5 

3.6 

3.6 

3.7 

196.9 

70 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

3.7 

3.8 

3.9 

4.0 

4.1 

4.2 

4.3 

4.4 

229.7 

80 

3.7 

3.8 

3.9 

4.0 

4.1 

4.2 

4.3 

4.4 

4.5 

4.6 

4.7 

4.8 

4.9 

5.0 

262.5 

90 

4.1 

4.3 

4.4 

4.5 

4.6 

4.7 

4.8 

4.9 

5.0 

5.2 

5.3 

5.4 

5.5 

5.6 

295.3 

100 

4.6 

4.7 

4.8 

5.0 

5.1 

5.2 

5.3 

5.5 

5.6 

5.7 

5.8 

6.0 

6.1 

6.2 

328.1 

no 

5.0 

5.2 

5.3 

5.4 

5.6 

5.7 

5.8 

6.0 

6.1 

6.3 

6.4 

6.5 

6.7 

6.8 

360.9 

120 

5.5 

5.7 

5.8 

6.0 

6.1 

6.3 

6.4 

6.6 

6.7 

6.9 

7.0 

7.2 

7.3 

7.5 

393.7 

130 

6.0 

6.1 

6.3 

6.4 

6.6 

6.8 

6.9 

7.1 

7.2 

7.4 

7.6 

7.7 

7.9 

8.1 

426.5 

140 

6.4 

6.6 

6.8 

7.0 

7.1 

7.3 

7.5 

7.7 

7.8 

8.0 

8.2 

8.4 

8.5 

8.7 

459.3 

150 

6.9 

7.1 

7.3 

7.4 

7.6 

7.8 

8.0 

8.2 

8.4 

8.6 

8.7 

8.9 

9.1 

9.3 

492.1 


COMPUTING THE MODIFIED INDEX OF REFRACTION, M 


87 


Table IOC. u for h from 150 in (492.1 ft) to 500 m (1,040 ft); F from 250 to 340. Values to be subtracted from F to 
obtain Fp = {n — 1) 10®. 


h (m) \ 

250 

260 

270 

280 

290 

300 

310 

320 

330 

340 

/ h (ft) 

150 

4.7 

4.8 

5.0 

5.2 

5.4 

5.6 

5.8 

6.0 

6.1 

6.3 

492.1 

175 

5.4 

5.6 

5.9 

6.1 

6.3 

6.5 

6.7 

6.9 

7.2 

7.4 

574.1 

200 

6.2 

6.4 

6.7 

6.9 

7.2 

7.4 

7.7 

7.9 

8.2 

8.4 

656.2 

225 

7.0 

7.2 

7.5 

7.8 

8.1 

8.3 

8.6 

8.9 

9.2 

9.5 

738.2 

250 

7.7 

8.0 

8.3 

8.6 

8.9 

9.2 

9.5 

9.9 

10.2 

10.5 

820.2 

275 

8.5 

8.8 

9.1 

9.5 

9.8 

10.1 

10.5 

10.8 

11.1 

11.5 

902.2 

300 

9.2 

9.6 

9.9 

10.3 

10.7 

11.0 

11.4 

11.8 

12.1 

12.5 

984.3 

325 

10.0 

10.3 

10.7 

11.1 

11.5 

11.9 

12.3 

12.7 

13.1 

13.5 

1,066.0 

350 

10.7 

11.1 

11.6 

12.0 

12.4 

12.8 

13.3 

13.7 

14.1 

14.6 

1,148.0 

375 

11.5 

11.9 

12.4 

12.8 

13.3 

13.7 

14.2 

14.7 

15.1 

15.6 

1,230.0 

400 

12.2 

12.6 

13.2 

13.7 

14.2 

14.6 

15.1 

15.6 

16.1 

16.6 

1,312.0 

425 

13.0 

13.5 

14.0 

14.5 

15.0 

15.5 

16.1 

16.6 

17.1 

17.6 

1,394.0 

450 

13.7 

14.2 

14.8 

15.3 

15.9 

16.4 

17.0 

17.5 

18.1 

18.6 

1,476.0 

475 

14.4 

15.0 

15.6 

16.2 

16.7 

17.3 

17.9 

18.5 

19.0 

19.6 

1,558.0 

500 

15.2 

15.8 

16.4 

17.0 

17.6 

18.2 

18.8 

19.4 

20.0 

20.6 

1,640.0 


Table lOD. u for h from 150 m (492.1 ft) to 500 m (1,640 ft); F from 340 to 420. Values to be subtracted from F to 
obtain Fp = (n — 1) 10®. 


\ F 
h(m)\ 

340 

350 

360 

370 

380 

390 

400 

410 

420 

(ft) 

150 

6.3 

6.5 

6.7 

6.9 

7.1 

7.3 

7.4 

7.6 

7.8 

492.1 

175 

7.4 

7.6 

7.8 

8.0 

8.2 

8.5 

8.7 

8.9 

9.1 

574.1 

200 

8.4 

8.6 

8.9 

9.1 

9.4 

9.6 

9.9 

10.1 

10.4 

656.2 

225 

9.5 

9.7 

10.0 

10.3 

10.6 

10.8 

11.1 

11.4 

11.7 

738.2 

250 

10.5 

10.8 

11.1 

11.4 

11.7 

12.0 

12.3 

12.6 

12.9 

820.2 

275 

11.5 

11.8 

12.2 

12.5 

12.8 

13.2 

13.5 

13.9 

14.2 

902.2 

300 

12.5 

12.9 

13.2 

13.6 

14.0 

14.4 

14.7 

15.1 

15.5 

984.3 

325 

13.5 

13.9 

14.3 

14.7 

15.1 

15.5 

15.9 

16.3 

16.7 

1,066.0 

350 

14.6 

15.0 

15.4 

15.8 

16.3 

16.7 

17.1 

17.5 

18.0 

1,148.0 

375 

15.6 

16.0 

16.5 

16.9 

17.4 

17.9 

18.3 

18.8 

19.2 

1,230.0 

400 

16.6 

17.1 

17.6 

18.1 

18.5 

19.0 

19.5 

20.0 

20.5 

1,312.0 

425 

17.6 

18.1 

18.6 

19.2 

19.7 

20.2 

20.7 

21.2 

21.8 

1,394.0 

450 

18.6 

19.2 

19.7 

20.3 

20.8 

21.4 

21.9 

22.5 

23.0 

1,476.0 

475 

19.6 

20.2 

20.8 

21.3 

21.9 

22.5 

23.1 

23.7 

24.2 

1,558.0 

500 

20.6 

21.2 

21.8 

22.4 

23.0 

23.6 

24.2 

24.8 

25.5 

1,640.0 


Table lOE. u for h from 150 m (492.1 ft) to 500 m (1,640 ft); F from 420 to 500. Values to be subtracted from F to 
obtain Fp = {n — \) 10®. 

\f / 


h (m)\^ 

420 

430 

440 

450 

460 

470 

480 

490 

500 

/ h{ii) 

150 

7.8 

8.0 

8.2 

8.4 

8.6 

8.7 

8.9 

9.1 

9.3 

492.1 

175 

9.1 

9.3 

9.5 

9.8 

10.0 

10.2 

10.4 

10.6 

10.9 

574.1 

200 

10.4 

10.6 

10.9 

11.1 

11.4 

11.6 

11.9 

12.1 

12.4 

656.2 

225 

11.7 

12.0 

12.2 

12.5 

12.8 

13.1 

13.3 

13.6 

13.9 

738.2 

250 

12.9 

13.2 

13.6 

13.9 

14.2 

14.5 

14.8 

15.1 

15.4 

820.2 

275 

14.2 

14.5 

14.9 

15.2 

15.5 

15.9 

16.2 

16.6 

16.9 

902.2 

300 

15.5 

15.8 

16.2 

16.6 

16.9 

17.3 

17.7 

18.0 

18.4 

984.3 

325 

16.7 

17.1 

17.5 

17.9 

18.3 

18.7 

19.1 

19.5 

19.9 

1,066.0 

350 

18.0 

18.4 

18.8 

19.3 

19.7 

20.1 

20.5 

21.0 

21.4 

1,148.0 

375 

19.2 

19.7 

20.2 

20.6 

21.1 

21.5 

22.0 

22.4 

22.9 

1,230.0 

400 

20.5 

21.0 

21.5 

22.0 

22.4 

22.9 

23.4 

23.9 

24.4 

1,312.0 

425 

21.8 

22.3 

22.8 

23.3 

23.8 

24.3 

24.9 

25.4 

25.9 

1,394.0 

450 

23.0 

23.6 

24.1 

24.7 

25.2 

25.8 

26.3 

26.9 

27.4 

1,476.0 

475 

24.2 

24.8 

25.4 

26.0 

26.5 

27.1 

27.7 

28.3 

28.9 

1,558.0 

500 

25.5 

26.1 

26.7 

27.3 

27.9 

28.5 

29.1 

29.7 

30.3 

1,640.0 



88 


METEOROLOGY— THEORY 


Table 11 A. Au for t* 9 ^ 0. Values to be inultiplied by /t X 10 2 and , r , I u for 


N 


i \ 

250 

260 

270 

280 

290 

300 

310 

320 

330 

340 

350 

360 

370 

±10 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.2 

0.2 

0.2 

0.2 

±20 

0.2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

±30 

0.3 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.5 

0.5 

0.5 

0.5 

±40 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.7 


*7 = temperature in degrees centigrade averaged from the ground to the height h. 


Table IIB. Su ior t* ^ 0. Values to be multiplied by A X 10“2 and from! ** ]l > O' 


N !•’ 


^ \ 

370 

380 

390 

400 

410 

420 

430 

440 

450 

460 

470 

480 

490 

500 

±10 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

±20 

0.3 

0.3 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.5 

±30 

0.5 

0.5 

0.5 

0.5 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.7 

07 

±40 

0.7 

0.7 

0.7 

0.7 

0.7 

0.8 

0.8 

0.8 

0.8 

0.8 

0.9 

0.9 

0.9 

0.9 


*t = temperature in degrees centigrade averaged from the ground to the height h. 



Table IIC. 

Aw for t* 

0. 

Values to be multiplied by h 

X 10“2 and 

j added to i f 

/subtracted from^ 

0 ^ 
V A 


\ 

t \ 

F 

250 

260 

270 

280 

290 

300 

310 

320 

330 

340 

±10 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

±20 

0.2 

0.2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

±30 

0.3 

0.3 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.5 

±40 

0.4 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.6 

0.6 

0.6 


*t = temperature in degrees centigrade averaged from the ground to the height h. 


Table IID. Aw fori* 0. Values to be multiplied by /i X 10 2 h-nd | fromf*^ ol^ ' 


\ F 


^ \ 

340 

350 

360 

370 

380 

390 

400 

410 

420 

±10 

0.1 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

±20 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.4 

0.4 

0.4 

±30 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.5 

0.6 

±40 

0.6 

0.6 

0.6 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 


*1= temperature in degrees centigrade averaged from the ground to the height h. 



Table HE. 

Aw for 1 * 

0. Values to be multii)lied by h X 10' 

.2 ^ , J added to ) 

t subtracted from 1 

0 0 

V A 



E 

420 

430 

440 

450 

460 

470 

480 

490 

500 

±10 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

0.2 

±20 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

0.4 

±30 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.7 

±40 

0.7 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.9 

0.9 


*i= temperature in degrees centigrade averaged from the ground to the height h. 


DIURNAL VARIATION OF THE GRADIENT OF MODIFIED M INDEX 


89 


DIURNAL VARIATION OF THE 
GRADIENT OF MODIFIED M INDEX^ 


The vertical gradient of modified refractive index 
depends on the vapor pressure and temperature 
gradients according to the formula^ 


dM 

dz 


79 /4800- O.MTWc 79 
T\ T ) dz 
/9600c ^ A dT 




+ 


t' dz)' 


Coefficients of vapor pressure and temperature gradi- 
ents are about 4.5 and 1.5 respectively. The third term 
gives a positive increase of 4 M units per 100 ft. In 
this paper^^'^^ the diurnal variation of the vertical M 
gradient will be inferred from the diurnal variation 
of temperature and humidity gradients. 


Temperature Lapse Rates over Land 

On clear nights with light winds temperature in- 
versions form in the lower atmosphere. The follow- 
ing characteristics of these inversions are to be noted. 

1. The inversion begins as a shallow layer near the 
ground before sunset, rises sharply after sunset and 
then more gradually to a maximum height at about 
sunrise. 

2. The temperature difference between two fixed 
levels in the first 100 ft of the ground is maximum 
shortly before sunset and oscillates about a slightly 
lower value the remainder of the night. (See Figure 
10 .) 

Observations at Leafield, England, and Potsdam, 
Germany, corroborate this. This phenomenon is prob- 
ably due to the more favorable humidity gradient in 
the early evening and to the heat of condensation re- 
leased by dew formation in the later night hours. 

Superadiabatic lapse rates characterize the lower 
atmosphere during clear days. The lapse rates in- 
crease sharply from sunrise to 3 or 4 hours after, 
gradually reach a maximum at about noon, and de- 
crease sharply after the time of the maximum tem- 
perature. 



TIME (GMT) 


Figure 10. Mean temperature variation on clear June 
days at Leafield, England. 


face to 1.5 C at 500 m. The night lapse rates over the 
ocean are therefore more unstable than the day lapse 
rates. Observations of the Meteor expedition in equa- 
torial regions revealed a mean inversion of 0.2 C in 
the first 9 m during the early afternoon, whereas in 
the early morning a mean lapse of 0.6 C was observed. 

6.6.3 Vertical Vapor Pressure Gradients 

At locations where a continuous supply of moisture 
on the ground is available, vapor pressure gradients 
follow evaporation processes and are maximum at the 
time of the maximum temperature at about sunrise. 
This diurnal course characterizes conditions over the 
sea, cloudy days over the land, and winter or rainy 
seasons over the continent. 

On clear days over the continent the vertical vapor 
pressure gradient is minimum at about sunrise, 
reaches a maximum in midmorning, and lowers to a 
secondary minimum at the time of the maximum tem- 
perature (in desert regions this is the principal maxi- 
mum shortly after sunset). Evaporation and mixing 
with drier air aloft govern this course. At night the 
soil absorbs moisture from the air causing a decrease 
in vapor pressure gradient. 

The seasonal and diurnal variation of vapor pres- 
sure gradient is illustrated in Figure 11. Maximum 
vapor pressure gradients are noted during April, the 
hottest time of year, and minimum in January. The 
oceanic type is represented by the curve for July in 
the rainy season. 


6 . 6.2 Xemperature Lapse Rates over the Sea 

The air over the sea has a greater diurnal range 
than the sea itself. Over the Sunda Sea this range 
has been observed to increase from 0.5 C at the sur- 

«By Raymond Wexler, Camp Evans Signal Laboratory. 

‘‘Symbols have same meaning as in preceding section, 
except that h is replaced by z. 


Vertical M Gradient 

Over the sea both temperature and humidity gradi- 
ents aid in causing a maximum of trapping during the 
day and a minimum during the night. The effect, 
however, is probably small. 

Over the continent, a minimum of trapping will 
exist in midafternoon. Thereafter both temperature 


90 


METEOROLOGY— THEORY 



Figure 11. Hourly vapor pressure difference, 6 to 46 ft 
at Calcutta. 


and humidity factors will cause a rise in the vertical 
M gradient to a maximum shortly after sunset. From 
that time to sunrise a decrease in the M gradient will 
occur. However, the height of the inversion continues 
to grow until sunrise, tending to cause an increase in 
the height of the duct. Whether a maximum or mini- 
mum of trapping will occur at sunrise will depend 
on whether the increase in the height of the inversion 
balances the decrease in vertical humidity gradient. 
It is probable that the humidity factor is the more 
important since the small magnitude of the tempera- 
ture increase in the upper portions of the inversion 
will seldom be sufficient to cause a decrease in M with 
height. After sunrise rising humidity gradients, par- 
tially balanced by falling temperature gradients, will 
cause a small maximum of M gradient at midmorning. 
Thereafter the M gradient will decrease to the after- 
noon minimum. 

The maximum and minimum decrease of M from 
6 ft to 46 ft, based on mean temperature and humidity 
data at Calcutta, India, are given in Table 12. 

In July the morning minimum and afternoon maxi- 
mum with small amplitude illustrate the oceanic type. 


The other months illustrate the continental type. Ac- 
cording to the table a maximum of trapping in India 
should occur in April just prior to the rainy season. 


Table 12. Decrease of M from 6 to 46 ft (Calcutta). 


Month 

A.M. 

Min Max 

Min 

P.M. 

Max 

Jan 

1 

4 

1 

6 

April 

7 

9 

5 

16 

July 

2 



6 

Oct 

1 

7 

3 

11 


^ 7 DETERMINING FLUCTUATIONS IN RE- 
TRACTIVE INDEX NEAR LAND OR SEA^ 

In connection with the rapid fluctuation or scintil- 
lation frequently observed in microwave reception, 
questions arise concerning turbulent atmospheric 
fluctuation at fixed points along the transmission 
path, particularly fiuctuations in refractive index. 
Rapid measurement of both temperature and humidity 
so as to give a direct determination of fiuctuation in 
refractive index is difficult. The purpose of this paper 
is to suggest that in certain cases the measurement 
of temperature fluctuation alone can give a good in- 
direct estimate of fluctuation in the modified index. 

The basic principle underlying this suggestion is 
that, if two initial kinds of air are mixed in different 
proportions, for all possible mixtures a fixed relation 
exists between any two properties conservative for 
adiabatic changes. 

To illustrate this, consider a diagram with poten- 
tial temperature and specific humidity as coordinates. 
Two initial kinds of air would be represented by two 
points on this diagram, and all mixtures of the two 
kinds would be represented by points on the straight 
line drawn between the two initial points. 

The practical case occurs when one point represents 
a large homogeneous mass of air, and the other a 
fixed boundary condition at the ground or water sur- 
face. The straight line then represents the mixtures 
that can occur in the vicinity of the boundary. For 
these the line shows specific humidity as a function 
of potential temperature. The relation between poten- 
tial temperature and potential refractive index could 
be shown by a similar diagram. 

Figure 12 shows some corroboration of this method 
and also how the method can be applied. This charac- 

‘By R. B. Montgomery, Radiation Laboratory, MIT. 


DETERMINING FLUCTUATIONS IN REFRACTIVE INDEX NEAR LAND OR SEA 


91 



Figure 12. Observations on February 24, 1945 at masthead of ship in Gulf Stream, wind 14 knots. Characteristic 
diagram. Vapor pressure over water is shown by lower bounding curve, over salt water by upper bounding curve. 
The family of curves gives modified index for 1,000 mb and zero height; or (n— 1)10^ for microwaves at 1,000 mb, zero 
height, where n is refractive index at /i = 0. 


teristic diagram has the same orientation as the 
Rossby diagram which is in routine meteorological 
use but with somewhat different coordinates. 

The ordinate is temperature and the abscissa is 
vapor pressure. A pair of curves gives the vapor pres- 
sure over fresh water and over sea water. The family 
of curves gives refractive index at radio frequencies 
and at a total pressure of 1,000 mb, or h = 0. 

On the diagram are plotted a few of a long series 
of determinations made by reading a sling psychrom- 
eter at half-minute intervals. These were recently 
obtained by the Woods Hole Oceanographic Institu- 
tion at the masthead of a ship crossing the Gulf 
Stream at a time when the air was much colder than 
the water. The water temperature was 70 F, fixing 
the boundary condition. The points lie fairly well 
on the straight line through the boundary value. They 
cover a range of 5 X 10"® in refractive index. Prob- 
ably a greater range would be indicated by a psy- 
chrometer having a more rapid response. 


It is seen that, whenever the fiuctuation in refrac- 
tive index at a point in the atmosphere is due to 
turbulent mixing between a large homogeneous mass 
of air and air controlled by a fixed boundary condi- 
tion, the fiuctuation may be obtained as follows: 
Measure the average temperature and humidity at this 
point and at the boundary, thus determining the rela- 
tion between refractive index and temperature. Meas- 
ure the fluctuation of temperature, from which the 
fluctuation of refractive index may be found from the 
established relation. 

It may be noted that the water temperature less 
the average air temperature gives a value for the 
temperature deficit. In the same way one may arrive 
at a humidity deficit and an M deficit (one million 
times the deficit of refractive index). Each of these 
quantities is represented on the diagram by the 
change from one end to the other of the line. It follows 
that the suggested method may be stated in terms of 
the relation that the ratio of temperature fluctuation 


92 


METEOROLOGY— THEORY 


to temperature deficit is equal to the ratio of humidity 
fluctuation to humidity deficit and very nearly equal 
to the ratio of M fluctuation to M deficit. 

6 » GRAVITATIONAL WAVES AND 
TEMPERATURE INVERSIONS ^ 

It has been noted that the guided propagation of 
microwaves is often accompanied by deep fades with 
periods of the order of a few minutes. The sugges- 
tion has been made that these fluctuations may be 
associated with atmospheric wave motion which could 
make the top of the duct an undulating surface rather 
than a level one.^®’^^ Therefore, it seems desirable to 
discuss, from a meteorological point of view, the pos- 
sibility of the existence of such atmospheric waves 
and the physical characteristics of any which might 
exist. The purpose of this paper is to review and sum- 
marize the meteorological information which is avail- 
able concerning the subject. 

A theoretical consideration of the problem indicates 
that atmospheric wave motion can occur at any sur- 
face in the atmosphere where there is a rapid change 
in wind velocity with height and a stable stratification 
of temperature. Such conditions are best fulfilled at 
temperature inversions, which, it will be noted, usu- 
ally correspond to a rapid decrease with height of the 
index of refraction. The wind shear supplies the 
energy to set up the wave motion, in the same way in 
which waves are formed at the surface of the ocean. 
Gravitation acts as a stabilizing or restoring force. 
Hence, these waves are of a mixed shearing and 
gravitational type. The waves may be stable or un- 
stable, depending on their wavelength, on the density 
and wind speed differences between the two media, 
and on the lapse rates in the two media. For any given 
values of the density and wind velocity differences 
and of the lapse rates, there is a critical wavelength 
below which wave motion is unstable; that is, it dis- 
appears into turbulent eddies because of the shearing 
effect. All wavelengths above this critical value will 
remain stable because of the gravitational effect. 
Hence one may speak of the former as ^‘shearing 
waves” and of the latter as ‘^gravitational waves.” It 
is the stable or gravitational type with which we are 
concerned. 

These considerations hold for wavelengths up to 
about 500 km. For longer wavelengths the effect of 
the earth’s rotation must be considered. In this paper 

jRy Lt. R. A. Craig, AAF, Weather Division. 


only the shorter wavelengths where this effect may 
be neglected will be discussed. 

A mathematical analysis of wave motion and deter- 
mination of the critical wavelengths involves a solu- 
tion of the equations of motion and continuity and an 
application of certain boundary conditions. In order 
to derive the critical wavelengths given below, the 
following assumptions have been made. 

1. The inversion or shearing layer may be re- 
garded as a strict discontinuity between the air above 
and the air below. This assumption is sufficiently ac- 
curate provided the thickness of the layer is small 
compared to the wavelengths which occur. 

2. The velocities associated with the wave motion 
are small compared with the undisturbed velocities 
of the air masses above and below the inversion. 

3. The height of the inversion above the lower 
boundary (ground) is equal to or greater than 40 
per cent of the wavelength which occurs. 

4. There is no friction between the two fluids. 

Two cases may be considered. The first is the case 

where the air masses are assumed to be incompressible 
and homogeneous. It also holds for two air masses 
with adiabatic lapse rates. In this case the critical 
wavelength is given by^®® 

2ir {U'-UYt't 

{T'-T)g T'+T 

In the second case the air masses are compressible 
and isothermal. For this case the critical wavelength 
is given by^® 

. _2ir{l/-Uy 


J(T'-T)^+2— (t'+T)^ — — 

^ kR 4 

In these two formulas, 

T' = temperature in the upper air, 

T = temperature in the lower air, 

Z7' = velocity in the upper air, 

U = velocity in the lower air, 
g = acceleration of gravity, 
k = Cp/Cv = 1.405, 

R = gas constant for air 

= 2.87 X 10® cmVsec® degree. 

In Table 13 the critical wavelengths in meters are 
tabulated for various values of wind shear and tem- 
perature difference. Values for the adiabatic case are 


ANALYSIS OF DUCTS IN THE TRADE WIND REGIONS 


93 


tabulated above values for the isothermal case. For 
an intermediate lapse rate some intermediate value 
holds. 


Table 13. Critical wavelengths in meters for T = 280°A. 


^T (C) 

0 

2 

AJJ (meters per second) 

4 6 8 10 12 

14 

0 


00 

00 

00 

00 

00 

00 

00 


0 

339 

677 

1016 

1354 

1693 

2031 

2370 

2 

0 

180 

718 

1616 

2872 

4488 

6463 

8796 


0 

159 

493 

860 

1225 

1584 

1938 

2287 

4 

0 

90 

359 

808 

1436 

2244 

3231 

4398 


0 

87 

317 

632 

985 

1351 

1720 

2087 

6 

0 

60 

239 

539 

958 

1496 

2155 

2933 


0 

59 

226 

479 

782 

1121 

1478 

1843 

8 

0 

45 

180 

404 

718 

1122 

1616 

2199 


0 

44 

174 

375 

634 

935 

1264 

1612 

10 

0 

36 

144 

323 

574 

898 

1293 

1759 


0 

36 

140 

308 

529 

793 

1090 

1413 

12 

0 

30 

120 

269 

479 

748 

1077 

1465 


0 

30 

118 

260 

451 

684 

952 

1247 

14 

0 

26 

103 

231 

410 

641 

923 

1256 


0 

26 

101 

225 

393 

600 

841 

1110 


Upper value: incompressible, homogeneous fluids. Lower value: com- 
pressible, isothermal fluids. 


Thus, for any given inversion, stable wave motion 
may exist so long as the wavelength is equal to or 
greater than the listed values and less than about 
500 km. There is no theoretical reason to believe that 
any particular wavelength in this wide range is more 
apt to occur in nature than any other. 

There is, however, some observational evidence to 
indicate that the wavelengths which occur in the at- 
mosphere are near the lowest possible values which 
can occur, namely, the critical values tabulated above. 
Billow clouds have been observed to occur near in- 
versions, and there are some ten cases on record where 
wavelengths of the billows as well as values for the 
temperature and wind velocity differences have been 
observed. In these cases the maximum difference be- 
tween observed wavelength and critical wavelength was 
48 per cent. In only three cases was the difference 
greater than 15 per cent.^®^ 

Other weather phenomena have been observed which 
indicate stable wave motion in the atmosphere. In 
1936, quite regular fluctuations were measured in 
ceiling height at San Diego on two occasions. The 
amplitude of the fluctuations averaged 25 to 30 m in 
the two cases, with periods of about 15 to 20 min over 
time intervals of 4 or 5 hours.^® In 1934 at the Blue 
Hill Observatory in Massachusetts, there occurred 
wave-like fluctuations in the pressure record, which 
were analyzed by Haurwitz.^^ In these cases upper-air 


data were not sufficiently accurate to compute wave- 
lengths quantitatively by means of the critical wave- 
length formula, but it appeared from approximate 
values of wind shear and density difference that the 
critical wavelengths might well be occurring. 

If it is desired, then, to predict what wavelengths 
will occur with a given inversion, the critical values 
would seem in the light of these observations to give 
a good estimate of the order of magnitude. 

Assuming that these wavelengths are the ones which 
occur, one can discuss the velocities and periods of 
the wave motion. For these critical wavelengths, the 
velocity of the wave motion is the mean of the veloci- 
ties of the air masses above and below the inversion. 
Hence the period can be estimated by dividing the 
wavelength given in the table by this value. As an 
example, for a mean velocity of 5 m per second, the 
periods vary from about 6 sec to about 8 min, de- 
pending on the wind shear and density difference. 

The vertical velocity at the inversion cannot be 
determined, since an arbitrary constant is involved. 
However, it can be said that this vertical velocity will 
be reduced to one-tenth its inversion value at a height 
d equal to 37 per cent of the wavelength above the in- 
version. This holds strictly only for the incompres- 
sible, homogeneous case but is approximately correct 
for the other case as well. 

It is known, then, from theoretical considerations 
and some observational material, that wave motion is 
apt to occur at a layer in the atmosphere where there 
is a temperature inversion accompanied by wind shear. 
When such inversions are believed to be of impor- 
tance in affecting the propagation of radio waves, it 
should be remembered that there may well be wave 
motion occurring and that the interface is not neces- 
sarily a level surface. It remains to be determined 
whether this fact will help to explain the observed 
very high frequency fading. An estimate of wave- 
length, period, and velocity of the atmospheric wave 
motion, as given by Table 13, may be of assistance 
in testing this possibility. 

^ ANALYSIS OF DUCTS IN THE TRADE 
WIND REGIONS'^ 

This report is an analysis of the frequency and 
magnitude of low-level and elevated ducts as indi- 
cated by meteorological observations over the trade 
wind areas of the Atlantic and Pacific Oceans. Mete- 

^By Raymond Wexler, Signal Corps Ground Signal Agency. 


94 


METEOROLOGY— THEORY 


orological soundings of the Meteor expedition,^^ taken 
during 1925 to 1927 over the Atlantic Ocean were 
utilized in analyzing elevated ducts. Climatological 
data of the Atlantic and Pacific Oceans were employed 
in study of low-level ducts. A qualitative analysis of 
95 soundings of the Meteor expedition had previously 
been made in reference 23. 

Elevated Ducts 

Trade Wind and Doldrums Areas 

A semipermanent high-pressure system is located 
over the oceans at about 30 degrees of latitude. The 
northeast trade winds blow from 30°N to about 5°N. 
Between the equator and 30° S the southeast trade 
winds prevail. The doldrums, a region of light winds 
and heavy rainfall, appears between the two wind 
systems. 

Ducts in the Trade Wind Eegion 

In the trade winds a warm, dry subsiding air mass 
exists over a cool, moist ground layer. The transition 
zone between the two air masses is characterized by 
a temperature inversion (increase with height) and 
a sharp decrease of the water vapor content of the 
air. It is this transition layer which coincides with 
the duct, which in this paper is defined as a layer in 
which the curvature of the path of high-frequency 
electromagnetic waves exceeds the curvature of the 
earth. Within these ducts these waves may be trapped, 
and abnormally long ranges may occur. 

As the trade winds blow toward the equator over 
warmer ocean areas the heating from below causes 
the duct to rise and to become weaker until finally 
near the equator the duct disappears and the two 
air masses become thoroughly mixed. 

Height of the Duct Base 

The base of the inversion (or duct) increases in 
elevation equatorward. According to the Meteor 
soundings, taken during March and April, the aver- 
age elevation of the base of the inversions rose from 
700 m at latitudes 15°N to 20°]Sr, to 1,020 m at 10°N 
to 15°N, and to more than 2,000 m at latitudes 5°N 
to 10°N. Between the equator and 5°N, no ducts 
existed to an elevation of 2,500 m. 

The elevation of the base of the inversion also in- 
creases westward into the Atlantic from the African 
Coast. At latitudes 15°N to 20°N, its elevation in- 
creases from less than 300 m off the African Coast 
to 1,500 m in mid- Atlantic. 


METERS 



Figure 13. Height of the temperature inversion base 
over the Atlantic. (After von Ficker.) 


Figure 13^"^ depicts the height of the temperature 
inversion base in the Atlantic, based largely on the 
data from the Meteor expedition. South of the equa- 
tor, soundings were made during the winter season 
(June to August), while north of the equator the 
soundings were made chiefiy in the spring (March 
to May). The height of the base of the inversion has 
a seasonal variation, being greater in winter than in 
summer. 

Figure 14 represents typical M curves computed 
from the soundings of the Meteor expedition. Curves 
A (sounding 182 of the Meteor expedition taken just 
off the African Coast) show a ground-based duct of 
elevation 140 m on the ascent curve and 90 m on the 
descent curve. Oceanward, the duct becomes ground- 
based, S-shaped, as is shown by curves B (sounding 
183). 



M 

Figure 14. M curves, Meteor expedition, March 1927. 


ANALYSIS OF DUCTS IN THE TRADE WIND REGIONS 


95 


The descent curve^ shows a decrease of 59 M units 
in 20 in, corresponding to a ray curvature about 20 
times greater than that of the earth’s surface. West- 
ward into the Atlantic the inversion base rises to about 
1,000 m. (Curve C, sounding 184.) 

Frequency of Duct Occurrence 

Within the trades proper a duct is practically cer- 
tain to exist. In Table 14 the percentage of duct 
occurrence, by latitude according to Meteor sound- 
ings, is tabulated. The extreme curve (ascent or de- 
scent) was utilized in determining the existence of a 
duct. 


Table 14. Frequency of duct occurrence by latitude 
over the Atlantic Ocean based on the Meteor soundings. 


Latitude, degrees 

Frequency (% of all cases) 

No. of cases 

20-15N 

100 

10 

15-lON 

71 

19 

10-5N 

40 

17 

5-ON 

0 

18 

0-5S 

0 

17 

5-12S 

56 

16 

12-18S 

53 

15 

18-24S 

73 

26 

24-35S 

10 

20 

35-50S 

19 

21 

50-63S 

0 

20 


It is evident from Table 14 that in the vicinity of 
the doldrums to 5°S) the existence of ducts is 

rare. A maximum frequency occurs between latitudes 
15° and 25°. Note that all soundings made between 
latitudes 15° to 20°N indicated the presence of a 
duct. 

Thickness of Ducts 

The average thickness of the duct in the trade 
wind inversion, according to Meteor data, is about 
130 m. According to the theory of the dissipation 
of the ducts near the equator due to heating from 
below, the thickness should decrease toward the equa- 
tor. No evidence of such a decrease was found from the 
Meteor soundings, probably because of the large height 
interval between observations. For this reason too, the 
figure for average thickness of 130 m is probably 
too large. 

Intensity of Ducts 

The decrease of the modified index of refraction 
within the duct averaged 28 M units between latitudes 

^The ascent and descent curves disagree largely because of 
the lag of the humidity element in the sounding rig. The curve 
showing sharper inversion is therefore probably the more 
accurate. 


10° to 20°N, and only 14 M units between latitudes 
5° and 10°N, indicating a decrease in the intensity 
of the duct equatorward. The intensity of the duct 
also decreases oceanward from the coast of Africa. 

Surface Ducts 

The thickness of surface ducts depends on the 
wind speed and the magnitude of the vapor pressure 
difference between the ocean surface and the air at 
some representative level (say the ship’s bridge). 
It is probable that the wind factor is the more im- 
portant. Near the west coasts of continents the low- 
ering of the trade wind inversion becomes the most 
important factor. Duct intensities over the ocean in 
the Northern Hemisphere, based on climatic charts 
of the ocean, have been computed by Montgomery and 
Burgoyne.^® 

Wind Speed 

According to observations taken in the Pacific 
north of New Guinea and northeast of Saipan, ducts 
were less than 10 ft in depth at wind speeds of one 
knot and were 40 to 60 ft at wind speeds of 10 to 20 
knots.^® According to climatic charts of the ocean 
(6), the average wind speed in the trade winds is 
maximum in summer at 15° to 20°N and in winter 
at 10° to 15°N. In the Southern Hemisphere maxi- 
mums are at 10° to 15° S in summer (December 
to February) and at 5° to 10° S in winter. These 
latitudes in the respective seasons should also coincide 
with the maximum thickness of surface ducts. 

Vapor Pressure Difference 

As the air flows toward the equator over continually 
warmer water surfaces moisture is being supplied to 
the air by evaporation from the water surface. Nearer 
the equator the increased rainfall decreases the water 
vapor pressure difference between the ocean surface 
and the air above. According to climatic charts^’^ the 
maximum vapor pressure difference between ocean 
surface and the air above in the trade exists at about 
latitudes 20° in summer (in both hemispheres) and at 
latitudes 10° to 15° in winter. This effect should also 
contribute to the existence of a maximum duct height 
in the trade winds at about 20° latitude in summer, 
15° in spring and fall, and 10° in winter. 

Surface Ducts near the Western 
Coasts of Continents 

All soundings of the Meteor expedition within 300 
miles of the coast of Africa showed intense ground- 


96 


METEOROLOGY— THEORY 


based ducts or S-sliaped ground-based ducts. These 
ground-based ducts are also a common occurrence on 
the west coast of the United States. At San Diego the 
average height of the inversion base is near 1,000 ft 
during the summer. The height of the duct base has 
a diurnal variation, being maximum in the morning 
at about 0800 local time and minimum at about 1600. 
The diurnal variations are governed by land and sea 
breeze phenomena. 

6.9.3 Experimental Evidence 

During 1944, aircraft traffic to and from Ascension 
Island at 8°S in the Atlantic was tracked by two 105- 
mc radars sited 2,500 and 1,700 ft above mean sea 
level. The following observed phenomena were re- 
ported verbally. 

1. Ranges were greater during the dry season than 
during the wet season. 

2. Ranges westward (270°) were greater than to 


the northeast (40°), and greater northeastward than 
to the north (10°). 

The decrease in duct intensity equatorward de- 
scribed herein is commensurate with observation (2), 
in which ranges are reported to be less toward the 
equator than along a parallel of latitude. 

Conclusions 

1. Over the trade wind areas of the oceans both 
elevated and surface ducts often exist. 

2. The elevated duct is of maximum intensity and 
frequency at 15° to 20° of latitude. It decreases in 
intensity and frequency equatorward, disappearing 
in the doldrums. 

3. The surface duct, dependent largely on wind 
speed, is of maximum depth at about latitude 20° in 
summer, 15° in spring and fall, and 10° in winter. 

4. Near the western coasts of continents the ele- 
vated duct lowers into an intense ground-based duct. 


Chapter 7 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 


7 1 METEOROLOGICAL EQUIPMENT FOR 
PROPAGATION STUDIES^ 

Outline of Problem 

E xpeeience gained during the last 2 years with 
radar, especially microwave radar, and with ex- 
perimental microwave communication equipment has 
shown that the electromagnetic radiation field pro- 
duced by a transmitter is subject to large variations 
depending on the weather. These variations are caused 
by refraction and so are related to variations of dielec- 
tric constant in the atmosphere. Pressure, temperature, 
and humidity determine the dielectric constant (re- 
fractive index). 

It has been found that above a certain height vari- 
able with season and geographical location but rarely 
exceeding 1,500 m above ground, atmospheric refrac- 
tion is reasonably constant. In the lower levels and 
especially in the lowest hundred meters of the atmos- 
sphere, temperature and moisture conditions strongly 
affect the radiation field and thereby influence the 
operation of radar and other short and microwave 
equipment. In order to evaluate this effect in quanti- 
tative terms, the temperature and moisture distribu- 
tion in the lowest layers must be determined with as 
high a degree of accuracy as is compatible with speed, 
ease of operation, and other practical limitations. 

A number of methods have been tried during the* 
past 2 years which range from measurements with 
ordinary radiosonde equipment to the use of a psy- 
chrometer on the steps of a fire ladder. Two facts have 
appeared rather clearly: First, hairs are not suitable 
for moisture measurements of this type on account of 
their great sluggishness (except perhaps for station- 
ary use on towers), since the time of adaptation of a 
hair to appreciable changes in humidity is of the 
order of 3 to 5 minutes. Secondly, it has been found 
that ordinary radiosondes are not usually appropriate 
because the readings obtained from them normally are 
taken about 100 m apart in vertical distance and for 
this particular problem a more detailed knowledge of 
the temperature and moisture distribution is necessary. 
With a clock-driven radiosonde this can be remedied 

“By W. M. Elsasser, Columbia University Wave Propaga- 
tion Group. 


by loading the sonde down by means of a ballast 
(water or sand) which slows down the ascent of the 
instrument in the lower levels. If the ballast is made 
to run out gradually, the full lift of the balloon may 
be restored at any given level. This method cannot be 
applied to the U. S. Weather Bureau radiosonde in 
which temperature and moisture data are sent out by 
a mechanism in which electric contacts are closed by 
a pressure cell at predetermined levels (see, however. 
Section 7.1.8, below). 

On the whole it has been found more advisable to 
develop new or improved instruments or to adapt spe- 
cial instruments for a low-level sounding technique 
rather than to rely on the existing facilities for aero- 
logical measurements. The methods developed so far 
involve the use of planes and dirigibles as well as cap- 
tive balloons and kites. For the lowest strata, specially 
built towers and ship installations have come into use. 

71.2 Wet and Dry Bulb Methods 

The use of humidity data for radio propagation 
problems involves new features in instrumental tech- 
nique because the main effects of strong refraction are 
found under approximately calm weather conditions. 
Therefore, when wet and dry bulb methods for humid- 
ity measurements are used, particular care must be 
taken to insure satisfactory aeration of the wet bulb. 
As a rule, an air speed of about 3 m per second ( about 
6.5 mph) is considered adequate ventilation for the 
wet bulb. In a plane, dirigible, or kite the necessary 
aeration is automatically provided. But on a tower 
or when carried by a captive balloon, artificial aeration 
will frequently be necessary. It has been claimed,** 
however, that if a wet bulb electrical resistor is used in 
conjunction with a captive balloon adequate aeration 
can be provided by giving the balloon cable a few 
violent jerks of about 5-ft amplitude. 

An ordinary sling psychrometer held out of the 
window of a fiying plane and aerated by the slip stream 
has been found to give fairly reliable results, provided 
the wet bulb is kept properly moistened. This method 
has been used with good success for preliminary re- 
search work. It may be presumed that the use of a 

^Data, courtesy of U.S. Navy Radio and Sound Laboratory, 
unpublished. 


97 


98 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 


rather slow-flying plane is essential, in order to keep 
the dynamic temperature correction small and also in 
order to insure a not too excessive rate of evaporation. 

Thermocouples, thermopiles, and temperature-sen- 
sitive resistors frequently are used as temperature 
responsive elements in place of actual wet and dry 
bulb thermometers. They are incorporated in spe- 
cially designed electrical bridge circuits in which the 
temperatures are read on either indicating or record- 
ing meters. 

7.1.3 Temperature and Humidity 
Resistance Elements 

Tempeeature 

Temperature-sensitive resistors are satisfactory both 
with regard to accuracy and the absence of lag. The 
British have used platinum resistance thermometers 
very successfully in stationary installations. In the 
United States electrolytic or ceramic resistance ele- 
ments are commonly used. The latter can be made to 
change their resistance several fold over a relatively 
narrow temperature interval. Their accuracy is there- 
fore limited, not so much by the accuracy of the cur- 
rent measurement as by their intrinsic stability after 
calibration, proper radiation shielding, etc. 

The electrolytic element developed for the Bureau 
of Standards radiosonde^*^ has a time-lag constant 
(time required to attain the fraction (1 — e~^) = 0.63 
of the total change) of 8 sec at an airspeed of 3 m per 
second, of 14 sec at an airspeed of 1 in per second, and 
of 40 sec in still air. 

Recently the ceramic Sanborn element® has come 
into use; it has about the same lag characteristics as 
the electrolytic element but is practically free from 
aging. The following time-lag constants have been 
measured 8 sec at an airspeed of 3 m per second and 
12 sec at an airspeed of 1 m per second. Another 
source reports 20 sec at an airspeed of 5 m per second 
(this value seems too large in comparison with the 
others) and 42 sec in still air. (Sec footnote b, pg. 97.) 

Moisture 

The Bureau of Standards resistance element as well 
as the Gregory humidiometer (a British development) 
uses a dilute solution of lithium chloride. 

In the Bureau of Standards element the lithium 
chloride film is deposited on the surface of a thin cyl- 
inder on which there is a bifllar winding of two thin 

“Manufactured by Paul H. Sanborn, 2602 Riverview Drive, 
Parkersburg, W. Va. 


wires. The stability and aging characteristics of this 
element are described in the literature.^’® An average 
actual accuracy of 5 per cent relative humidity is 
claimed for the ordinary radiosonde when used under 
routine conditions. Higher accuracy (1 per cent RH) 
is claimed, at least at temperatures above freezing, 
when used with captive balloon equipment,®^ partially 
because the current is frequently reversed to cut down 
polarization effects and partially because the calibra- 
tion can be more closely watched. Tests® show that at 
an airspeed of 2.5 m per second the time lag constant 
is 3 sec at 24 C and 11 sec at 0 C. 

The Gregory humidiometer’*’® uses a lithium chlo- 
ride solution soaked in a clean cotton cloth. The re- 
sistance of the element changes from over 100,000 
ohms at 30 per cent RH to as little as 50 ohms at 100 
per cent RH. It undergoes pronounced aging during 
the first several days and then remains sensibly con- 
stant for a number of weeks. The instrument is in an 
experimental stage and is at present being tried out at 
the Rye towers in Sussex (see Section 7.1.6, below). 

Circuit Design for Resistor Elements 

Thermocouples or thermopiles are commonly used 
in a conventional bridge circuit. In connection with 
the electrolytic and ceramic type of resistance ele- 
ments, circuits have recently been developed that in- 
clude certain features novel in the technique of atmos- 
pheric measurements. 

In the equipment developed by Washington State 
College®*^ the standard radiosonde temperature ele- 
ment was originally used, but in a more recent type 
^they have combined the Sanborn temperature element 
and the radiosonde electrolytic humidity element. The 
electric equipment (Figure 1) consists of a dry cell 
with potentiometer supplying about volt, two 
double-pivot microammeters, one in series with each 
of the elements, and a 6-volt d-c motor. The relay re- 
verses the current through the elements at a rate of 
50 cycles (100 reversals) per minute while maintain- 
ing constant polarity at the meters. The current is 
smoothed by large condensers in parallel with the 
meters. The commutation eliminates polarization of 
the electrolytic elements and greatly increases their 
accuracy and useful life. The commutation period is 
so selected that it is long enough to prevent inductive 
and capacitative interaction between the two circuits 

‘^Information supplied to the U. S. Propagation Mission to 
England. 

“Instruments made by Negretti and Zamba, Ltd., London. 


METEOROLOGICAL EQUIPMENT FOR PROPAGATION STUDIES 


99 



MOTOR 

60 R PN4 



j 






RELAY 


6 V DC 


Figure 1. Wired sonde circuit. 

The potentiometer P applies a constant voltage (0.36 v at low and 0.18 v at high RH) to both of the independent circuits of the sonde proper. 
The currents, determined by the resistances of the relative humidity and temperature elements respectively, are read on the RH meter and 
T meter. S 3 commutates these currents at half-second intervals; Si and S 2 , actuated simultaneously with S 3 , maintain constant polarity at the 
meters. The l,000-/if condensers CC smooth the currents through the meters. S 1 S 2 S 3 are contained in the pile-up of a single relay which is actuated 
by a miniature worm-geared motor as shown. The 10,000-ohm protective resistance R is shorted out during measurement. Connections to the 
ground end of the cable are made through slip rings (not shown) mounted on the cable reel. All components, excepting the sonde, cable, and 
6-v storage battery, are housed in a single case 20x9x7 in. 


but is short enough to allow of smoothing the currents 
through the meters. 

The circuit illustrated in F'igure 2 has been devel- 
* oped by the Propagation Group at the Radiation Labo- 
ratory, MIT.^ The apparatus includes two Sanborn 
resistance elements, one of them surrounded by a mois- 
tened wick. The current flowing through the resistors 
originally was fed into an amplifier which drove a 
recording milliammeter. However, after a number of 
amplifiers had been tried, the simple scheme shown in 
Figure 2 was adopted and, at the time of the writing 
of this report, is being used for all measurements made 
by the Radiation Laboratory, those from planes as 
well as those from captive balloons which will lie 
described later. 

The dry and wet elements are placed in the circuit 
alternately by means of a hand-operated switch. The 
device can be calibrated by means of a set of fixed 


precision resistors and the balance of the bridge is 
checked before each flight. An advantage of this 
method is the possibility of using a commercial d-c 
recorder (0 to 1 ma) immediately at the plate ter- 
minals of the amplifier tube. This is particularly 
favorable for use in airplanes and dirigibles. 

It is well known that the ordinary thermocouple is 
not readily adapted to recording purposes. Only at sta- 
tionary installations such as towers, where multi- 
junction thermopiles can be used, is it possible to 
record the indication of the sensitive galvanometers 
required. 

Anemometers 

Wind measurements are of importance in connec- 
tion with off-shore winds at coasts which give rise to 
pronounced refraction of short and microwaves. The 
ordinary commercial anemometers become quite un- 


100 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 



Figure 2. Schematic circuit of electronic amplifier. 

The resistance of the thermal element, X, controls the bias of one triode of the double triode, 6SN7, which acts as a vacuum tube voltmeter 
to compare the resistance of the thermal element with a standard resistance. A 1-ma recording meter s placed between the two plates. The 
resistance in the grid circuits is so chosen as to place 10 v across the thermal element at the lowest temperature of each range. This voltage 
decreases as the temperature rises. The zero is set by means of a lOD-ohm potentiometer in the cathode circuit. Calibration of the amplifier is 
obtained by switching a series of precision resistors in steps of 1,003 ohms into the circuit in place of the thermal element. A range of roughly 25 C 
for full scale is used, and changes of 0.25 C can be measured. Sufficient overlapping is provided so that both wet and dry bulbs can record on 
a single setting. 

The stability is such that with a change in line voltage between 95 and 120 v there is no readable change in the meter deflection at 0 (when the 
tubes are balanced) or at full scale reading. When tubes are replaced there is, at worst, a change of 1 per cent of full scale deflection tapering to 
no deflection at 0. 


reliable at very low wind speeds (of the order of V 2 idi 
per second) and may stop completely. A special ane- 
mometer for low wind speeds® has been designed by 
the British Chemical AVarfare Service and is used as 
a regular piece of field equipment by its units. In the 
United States a highly sensitive anemometer has been 
developed at the California Institute of Technology.'^ 
This instrument records wind speeds from 0.5 to per- 
haps 30 mph. It has the conventional three cups rotat- 
ing on a vertical axis. Each rotation is registered on a 
counter by magnetically operated electrical contacts. 
For higher wind velocities the counter may be switched 
to record only every hundred rotations. The apparatus 
is delicate and is critical in its behavior toward certain 
adjustments. 

Semipermanent Installations 

Towers 

Two major installations of towers are at present in 
existence in England. They are the Porton towers and 
the Rye towers. The Porton towers on the Salisbury 
Plain form part of the extensive meteorological equip- 
ment of the British Chemical Warfare Service and 


have been in use for a considerable number of years.® 
Continuous records of dry and wet bulb temperatures 
at heights of 4, 23, and 56 ft above the ground are 
made. The elements used are platinum resistance 
thermometers connected into bridge circuits and are 
artificially aerated. The recording mechanism is lo- 
cated near the bottom of the tower. 

A similar set has recently been installed on the Rye 
towers in Sussex which form part of a CH radar sys- 
tem. Temperature and relative humidity are recorded 
for heights of 4, 50, 155, and 360 ft above ground. The 
resistance thermometers are similar to those at Porton, 
but the moisture measurements are made with the 
Gregory humidionieter described above. 

In a large research project on microwave refraction 
carried on in the summer of 1044 by the Propagation 
Group at the Radiation Laboratory, a mast was erected 
at one terminal of the path. Wet and dry bulb tempera- 
tures are recorded continuously with the device de- 
scribed in Section 7.1.4 at heights of 4, 16, 36, and 
55 ft above the sea surface, these heights varying some- 
what with the tide. The measuring elements are lo- 
cated in one end of a horizontal piece of tubing 3 ft 


METEOROLOGICAL EQUIPMENT FOR PROPAGATION STUDIES 


101 


long, and in the other end, close to the pole, an aera- 
tion fan is mounted. Wind velocity records are made 
by means of Stewart anemometers. 

Ships 

The Eoyal Navy has detailed three yachts for atmos- 
pheric measurements on an experimental microwave 
transmission path over the Irish Sea. They are pro- 
vided with dry and wet thermocouples at altitudes of 
5, 10, 40, and 50 ft above sea level. The former two 
are mounted on hinged beams outboard, while the 
latter two are on a mast in the forward part of the 
ship. The thermocouples are copper-constantan, and 
there are two in series for the temperature measure- 
ment with the cold junctions placed in a Dewar flask 
filled with melting paraldehyde (maintaining a tem- 
perature of 50 F). There are two pairs of dry and wet 
junctions connected in series which measure the wet 
bulb depression. The galvanometer is in the ship’s 
cabin. Aeration is provided by the ship’s movement, 
and when measurements are made the ship sails into 
the wind to mijiimize the effects of the discharge from 
the smokestack. 

In the project at the Radiation Laboratory just re- 
ferred to measurements are also being made from the 
mast of a boat. The 48-ft mast is provided with a 6-ft 
cross arm and a motor-aerated housing containing the 
elements can be raised from the bottom of the mast 
to the end of the cross arm, giving continuous infor- 
mation over the height of its. travel. 

Measurements carried out on shipboard by means 
of captive balloons or kites will be discussed in Sec- 
tion 7.1.8. 

7.1.7 Measurements on Board Planes 
and Dirigibles 

As has been mentioned before, a sling psychrometer 
held out of the window of a flying plane will give 
reasonably accurate results if some elementary pre- 
cautions are taken to insure proper moistening of the 
wick. 

The two types of instruments described in Section 
7.1.4 have been adapted for use with airplanes. In the 
Radiation Laboratory instruments the two elements are 
mounted diagonally in a piece of Bakelite tubing about 
iy 2 in. in diameter, the dry element in front of the 
wet element, relative to the wind stream. In the earlier 
airplane measurements water was blown over the moist 
element and a reading made when the recorder showed 
equilibrium to be reached. Now capillary action is used 


throughout, the water being supplied from a small 
vessel underneath the Bakelite tube. This instrument 
has been tested in a wind tunnel with wind speeds up 
to 145 mph. The dynamic pressure effect increases 
the reading by 0.4 C at the cruising speed of the plane 
(100 mph). This value was checked, both in the plane 
itself and in a wind tunnel. 

The Washington State College [WSC] instrument 
has been adapted for airplane measurements and has 
been used on several types of planes during tests in 
Panama. The elements were housed in a single- 
walled cylinder of aluminum, about 1.75 in. in diam- 
eter, covered on the forward end with a cone. A small 
circular opening (% in. in diameter) made by cutting 
off the end of the cone reduced the velocity of the air 
across the elements to about one twenty-second of the 
plane’s speed. Comparison of a plane sounding and a 
balloon sounding in the same region at the same alti- 
tude and time gave identical results within reasonable 
experimental error. 

With airplane measurements the determination of 
the plane’s altitude becomes an important task. In 
the experimental flights at the Radiation Laboratory 
the altimeter of the plane itself was used. According 
to the experience obtained in Panama it is desirable 
to have an additional altimeter placed directly before 
the operator in order to facilitate rapid and accurate 
altitude determinations. The nominal accuracy of an 
airplane altimeter is about 20 ft. Over sea it may be 
possible to determine the absolute altitude of the 
plane with about the same degree of accuracy, but 
over land less accuracy is to be expected. 

Measurements from a dirigible (blimp) have been 
carried out by Radiation Laboratory. The instrument 
is suspended on a cable about 100 ft below the ship. 

Captive Balloon Sondes and Kites 

Radio Transmission Type 

Two different methods have been tried in connec- 
tion with balloons and kites. When first used in prac- 
tice an ordinary radiosonde was attached to the balloon 
(kite) and the results were recorded on the ground 
by radio in the usual way. This method was used in an 
experimental investigation carried out under the aus- 
pices of the AAF Board, Orlando, Fla.® Although by 
the nature of the instrument the measurements are 
spaced 200 to 300 ft apart, a rough survey of the 
temperature and moisture distribution sufficient for 
some operational purposes was gained in this way. 


102 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 


The record on the ground was taken by means of a 
standard U. S. Army radiosonde receiver. 

It was pointed out in this report® that it might he 
advantageous to use a combination of two radiosondes 
in tandem, such that in one instrument the contacts are 
connected to the temperature device, in the other to 
the humidity element. It would then be possible to ob- 
tain simultaneous temperature and moisture readings 
at the same elevation, instead of alternating ones, as 
is the case when only one instrument is used. This 
would, however, require the use of two receivers at 
the ground with two slightly different carrier fre- 
quencies. 

Another adaptation of the standard Weather Bu- 
reau radiosonde was made by WSC.®^ The ground in- 
stallation was similar to that used by the Weather 
Bureau in its full radiosonde measurements, but the 
standard radiosonde was modified by replacing the 
pressure- (altitude-) actuated switch by a clock-driven 
commutator. The results obtained were quite satisfac- 
tory, and the technique may be appropriate at stations 
where standard radiosonde equipment is available. 

WiKED Tkansmission Type 

The other captive balloon or kite instruments are 
of the wired type with galvanometers or recorders at 
the ground. They may be classified as light and heavy 
types. The light instrument merely carries tempera- 
ture and humidity elements aloft which together with 
the radiation shield do not weigh more than a few 
ounces. To this is added the weight of the cable or 
string carrying the connecting wires. The heavy in- 
strument carries its own aeration equipment in the 
form of a fan driven by a small electric motor. The 
fan and the heavier construction of the frame required 
to accommodate it increase the weight of the airborne 
unit to several pounds. In addition there must be at 
least one more lead on the cable to supply power to the 
fan. 

The first captive balloon instrument was built in 
England about 2 years ago.^® The balloon is anchored 
by an electric cable and the instrument is provided 
with a fan. The overall weight of the instrument with- 
out cable is about 8 lb. Its main part is a piece of poly- 
thene tubing in the shape of an inverted Y with the 
fan placed on top of the tubing while the two legs of 
the Y contain the dry and wet thermopiles. The latter 
are four- junction copper-constantan combinations. 
The cold junctions are enclosed in a small Dewar flask 
filled with melting ice which is located about 10 in. 
below the Y piece. 


The cable of this instrument has five leads, three 
for the thermocouples and two for the fan (2 to 4 
volts of direct current) ; the instrument is suspended 
from the balloon proper by means of a 100-ft string 
which minimizes the influence of irregular motions of 
the balloon upon the instrument. The ground equip- 
ment consists of potentiometers and a spot galvanom- 
eter with a switch to alternate between the dry and 
wet couples. 

The light type of balloon or kite sounding equip- 
ment was first developed by The tempera- 

ture and humidity elements are surrounded by a 
double-walled aluminum radiation shield, and the 
whole airborne assembly weighs only a few ounces. 
Originally the standard AYeather Bureau temperature 
element was used ; now they use the Sanborn element 
together with the Bureau of Standards humidity ele- 
ments in the circuit shown in Figure 1. 

The sounding procedure used with this instrument 
consists in letting the balloon go rapidly up to a max- 
imum altitude chosen so high that moisture and tem- 
perature variations with height are comparatively slow. 
The characteristic features of the atmospheric stratifi- 
cation lie below this level. A rough survey of this 
stratification is made during the ascent. The instru- 
ment is then reeled in and is stopped at a number of 
predetermined levels, long enough to let the elements 
reach equilibrium with the surrounding air. The levels 
chosen are spaced at height intervals small enough so 
that the readings taken reveal the atmosphere struc- 
ture accurately. It has been found that rapid lowering 
of the sonde between readings will provide sufficient 
aeration of the elements to give quite accurate readings 
even in completely calm weather. 

The balloon sonde of the Navy Radio and Sound 
Laboratory uses a dry and a wet Sanborn resistor 
surrounded by a double-walled aluminum radiation 
shield. Often wind aeration is found to be sufficient for 
the wet bulb element, but in calm air the instrument 
is aerated before readings by giving the cable a series 
of rapid jerks of about 5-ft amplitude. The ground 
equipment consists of a 0 to 50 microammeter which 
can be connected to the dry element, the wet element, 
and a standard resistor in turn by means of a double- 
pole triple-throw switch. Voltage is supplied by a dry 
cell and potentiometer. 

The captive balloon sondes used by Radiation Labo- 
ratory^ employ dry and wet Sanborn resistors mounted 
diagonally in a piece of Bakelite tubing surrounded 
by an aluminum radiation shield. The circuit and am- 


METEOROLOGICAL EQUIPMENT FOR PROPAGATION STUDIES 


103 


plifier liave been described in Section 7.1.4. In the 
lightweiglit wind-aerated instriiinent the piece of 
Bakelite tubing containing the resistors is horizontal. 
Owing to the shape of the aluminum shield it will take 
up an orientation in the wind such that the air strikes 
the dry element before the wet element. More fre- 
quently, however, they use a heavier, fan-aerated in- 
strument in which the Bakelite tubing is vertical and 
the fan is placed on top of the assembly. This instru- 
ment has been extensively used in the recent experi- 
ments at the New England coast ; either it was attached 
to a barrage balloon (35-lb lift), or in calm weather to 
a large Neoprene balloon (see Section 7.1.8). The 
latter type of balloon was also used to make ascents 
from a boat in light and moderate winds. 

Recently, a type of captive balloon equipment has 
been developed com merci ally “ which uses the standard 
United States radiosonde recording equipment as the 
ground component. The airborne component consists 
of an audio relaxation oscillator with the measuring 
element connected in the grid circuit. Changes in the 
measured temperature or relative humidity alter the 
frequency developed by the oscillator. By means of a 
special attachment on the ground the balloon sonde is 
used in connection with the regular radiosonde receiv- 
ing and recording equipment. The airborne component 
includes dry cells for the operation of the oscillator 
and the weight of the airborne unit is about 2 lb. 

Cable and Balloon Technique 

The cable which connects the measuring elements 
aloft to meters on the ground is one of the most critical 
parts of the wired sonde. The earliest British instru- 
ment^® used a cable obtained by stranding together 
thin, insulated, flexible copper cables; the weight is 
about 21/2 lb per 100 ft. Similar cables were used for 
a while by Radiation Laboratory ; later on they changed 
to the types of cable to be described presently. 

WSC developed a cable technique^^*®*’ in which 
the pull of the balloon or kite is taken up by a strength 
member such as strong linen twine. Eishline, breaking 
strength 64 lb, was originally used.^^ Three No. 30 
enameled copper wires are wound around the strength 
member with a pitch of several inches. After being 
made up the cable was passed under thinned airplane 
dope to cement it together and make it waterproof. 
The weight of this cable is about 1 lb per 1,000 ft. 

Later developments in this cable resulted in three 
types that have survived accelerated tests equivalent 
to 1 year’s exposure to salt spray without developing 
serious leakage.®'’ 


Tyi)e A consists of a braided Eiberglas strength 
member (nominal strength 80 lb), three No. 30 For- 
mex-insulated copper wires, and a braided nylon sheath 
impregnated with vinyl plastic.^ 

Type B has an enameled stainless steel strength 
member (nominal strength 40 lb) and three Formex 
conductors within an impregnated nylon sheath.® 

Type C is similar to Type A but has a 180-lb test 
Fiberglas strength member; it is used with large kites.* 

These cables are wound around the drum of an ordi- 
nary winch, and the conductors are connected to the 
ground equipment by means of slip rings mounted on 
the winch. 

It has been found advantageous, especially for the 
heavier instruments, to suspend the instrument from 
the balloon on a 100-ft flshline; this line acts as a 
buffer in protecting the instruments from sudden 
jerks of the balloon. 

Neoprene balloons'’ are recommended in preference 
to rubber latex balloons. They have a much longer 
useful life than rubber balloons and give warning be- 
fore breaking by becoming misshapen. The 300-g N-4 
balloon is used in connection with the WSC instru- 
ment.®*’ The N-700 balloon has been used by Radiation 
Laboratory for the fan-aerated instrument. Barrage 
balloons (lift 35 lb) were also successfully used in 
winds slightly in excess of those that permit the use 
of lighter balloons. 

The light type of balloon becomes unmanageable in 
winds above about 6 to 8 miles per hour. A two-reel 
technique has been developed®*’ to extend the use of bal- 
loons to somewhat higher wind speeds (from 6 to 10 
mph) . The pull of the balloon is taken up by a separate 
fishline, the reel of the fishline being placed windward 
relative to the reel of the cable (Figure 3). 

In wind speeds above about 8 mph kites are used in 
place of balloons. A small folding kite', standard for 
“^Gibson Girl” emergency radio equipment, is easy to 
handle and requires only a light cable, but its ceiling is 
limited to about 400 ft. This type of kite has been used 
successfully for soundings from boats. 

A heavier, 7-ft kite^ is well adapted to land-based 
soundings. It flies at a high angle (55° to 60°) and 
can be put up at minimum wind speeds. At the high 
relative wind speeds encountered in ship-based sound- 

'Supplied by International Braid Co., Providence, R. I. 

^Supplied by Boston Insulated Wire and Cable Co., Boston , 
Mass. 

''Supplied by the Dewey and Almy Co., Cambridge, Mass. 

‘Supplied by Hoffman Radio Co., Los Angeles, Calif. 

^Supplied by F. C. Seyfang, Atlantic City, N. J. 


104 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 



Figure 3. Sounding techniques for use at the wind speed ranges indicated. 


Temperature and humidity elements mounted within the radiation shield S are connected through the 3-conductor cable C with slip rings on 
the cable reel R. The meter box (not shown) is connected to the brushes of R. B: 300-g Neoprene balloon. L: light fishline. F: fishline reel. SK: Sey- 
fang 7-ft kite. N: nylon kite line. W: kite winch. HK: Hoffman single cell box kite. Arrangement (D) is suitable for sounding from moving ships; 
its ceiling is limited to about 400 ft by the small lift of this kite. 


iiigs the pull of this kite is excessive and launching cor- 
respondingly difficult. 

Sounding techniques are shown schematically in 
Figure 3. For the kite a braided, waterproof nylon 
line, breaking strength 150 lb. is recommended. For 
ship-based soundings or conditions where sudden high 
stresses are likely, a 300-lb test nylon line may be used. 

There seems to be no difficulty in measuring the 
altitude of the captive balloon or kite.®^ The length 
of line paid out is determined either by counting the 
turns of the reel or by means of markers attached to 
the cable at regular intervals; if the line is off the 
vertical, its mean inclination can be measured with 
sufficient accuracy by a simple hand inclinometer. 

72 AUTOMATIC RECORDING OF 
METEOROLOGICAL SOUNDINGS^ 

A means has been developed for making automatic 
recordings on a Leeds and Northrup Speedomax or 
Friez Cycloray recorder of low-level meteorological 
soundings of temperature and humidity. The design 
of the equipment has been restricted in the sense that 
the standard Weather Bureau- Army-Navy electrolytic 
hygrometer and negative resistance temperature units 
must be utilized ; all recordings must be made on the 
existing automatic radiosonde recorders just named. 

E. Dillon Smith, U. S. Weather Bureau, Washington, 

D. C. 


General Design Considerations 

The existing standardized electrolytic hygrometer 
strip polarizes when direct current is placed on its 
terminals. However, if a reversed direct current is 
placed on the terminals of the strip, this polarization 
tendency is neutralized. This would seem to indicate 
the desirability of placing a low-frequency alternating 
current on its terminals in lieu of the direct current 
commutation principle which generally has been used 
in existing low-level meteorological sounding equip- 
ment. 

The frequency of the alternating current to be 
placed on the strip will in general be controlled by the 
reactance of the low-level sounding cable. In view of 
this limitation a frequency of approximately 10 c has 
been used. 

The temperature resistor operates equally well on 
either direct or alternating current; therefore, it re- 
quires no equipment design considerations. 

Electrical Characteristics of Elements 

Present practice makes the ^dock-in’^ for the tem- 
perature and humidity elements through a resistor in 
series with the elements. However, this technique in- 
troduces errors in the readings both above and below 
that for the lock-in point. Effectively, the slopes of 
the calibration curves are altered, affecting the read- 
ings on the indicators. In view of this situation, it is 
fundamental that voltages should be measured across 



RECORDING OF METEOROLOGICAL SOUNDINGS 


105 



Figure 4. Basic components of amplifier-recorder. 


the hygrometer or temperature elements. Any lock-in 
device must be inherent in the equipment as remote 
from the voltage appearing across the elements. This 
principle has been incorporated in the design of the 
equipment. 

Since the electrolytic hygrometer element can be 
designed so that it will not polarize under direct cur- 
rents approaching 100 /xa, it appears desirable to design 
the recording equipment for possible adaptation to 
this type of element. In other words, the amplifiers 
must be capable of handling direct currents as well as 
alternating currents. 

Cable Ekkor 

If the standard temperature and hygrometer curves 
are used originally for calibrating the recorder, it is im- 
portant to note that the cable resistance will introduce 
a positive error. For average Southwest Pacific climate 
and sounding heights up to about 3,000 ft, the positive 
temperature error is roughly 1.5 F while the positive 
hygrometric error is aliout 5 per cent RH. 

These errors, unfortunately, cannot be compensated 
without complete recorder calibration at the outset or 
by mathematically adjusting the standard calibration 
curves. Thus, since the cable is a fixed resistance, the 
standard curve can be recomputed to allow for any 
fixed cable resistance, with the result that no error 
will be introduced into the recorder. 


In consideration of the above requirements, it will 
be necessary, in adapting the standard U. S. Weather 
Bureau electric hygrometer and temperature elements, 
to provide (1) a means of developing a stable low- 
frequency voltage across the elements, (2) to switch 
from one element to another in measuring the voltages 
across these elements, (3) to amplify such voltages, 
(4) to provide a means of controlling the sensitivity 
and range of the recorder, and ( 5 ) to supply the output 
of the amplifier to a 0 to 500 microammeter auto- 
matic recorder. 

Electronic Amplifiers 

The basic components of the amplifier-recorder are 
shown in Figure 4. The frequency generator operates 
at 10 c and is composed of three units, (1) a phase- 
shift oscillator, (2) a paraphase amplifier, and (3) a 
controllable push-pull output amplifier. 

The amplifier-recorder unit is composed of (1)' a 
series limiter, (2) a cathode follower, and (3) a two- 
story amplifier, as shown in Figure 5. For the sake 
of simplicity, the automatic switching device that 
changes the current from hygrometer to temperature 
element has been shown schematically. The switching 
takes place at any rate between approximately 1.0 to 
0.1 c; this rate is not critical. 

Since the amplifier must be able to handle either 
direct or alternating current, the balanced two-story 



106 


METEOROLOGICAL EQUIPMENT FOR SHORT WAVE 


amplifier has been constructed, wherein the top tube 
is the plate load for the lower tube of the two-story 
amplifier. The output of this amplifier is approximate- 
ly equal to one-half the amplification factor of the tube. 

As shown in Figure 5, this amplifier is fed by a 
cathode follower which has impressed upon it from the 
series limiter only the positive peaks of the a-c voltage 
drop across the hygrometer or temperature element. 
The voltage across the elements can be as low as ^ 
to y< 2 . V, depending upon the sensitivity adjustment of 
the amplifier. It will operate with voltages as high 
as 30 to 60 V across the elements. 

Reducing Amplieiek Output to Ground 

The amplifier output is at one-half the positive volt- 
age of the plate supply above ground. However, this 
output can be reduced to ground by the introduction 
of a cathode follower or more simply by three series 
sections of a resistor and glow tube connected in series. 
The output of the two-story amplifier is fed into the 


junction between the first and second sections while 
the output is taken from the junction of the second 
and third sections, where the first section is connected 
to the positive plate supply and the third section con- 
nects to a negative potential equal to one-half the posi- 
tive voltage. It is not necessary to make this addition 
to the present equipment. 

Recorder Accuracy 

It is possible to measure temperatures to less than 
1/4 of a degree Fahrenheit and humidities to less than 
V 2 of 1 per cent. However, this accuracy is not neces- 
sarily required for low-level atmospheric soundings 
and construction of M curves. 

Conclusion 

Direct automatic recording of low-level temperature 
and hygrometer readings is suggested. The method is 
especially adaptable for fixed or shipboard station 
operation. 


Chapter 8 

METEOROLOGY— FORECASTING 


8 1 FORECASTING TEMPERATURE AND 
MOISTURE DISTRIBUTION OVER 
MASSACHUSETTS BAY ^ 

B efoke going into a description of the forecast 
program and results it will be profitable to describe 
the method used in coordinating the observations. 

8.1.1 Meteorological Observations 

Soundings were made according to two major 
plans. The first was in conjunction with the radio 
path. According to that plan, airplane soundings were 
made once or twice a day at two or three points along 
the transmission path. The boat would take either 
mast or balloon soundings along the path while meas- 
urements at Race Point Light (Provincetown) would 
continue at 2 - to 4-hour intervals during most of the 
day and sometimes at night. The Race Point Station 
had the advantage of being well away from land (for 
all but easterly winds) and soundings there would 
thus represent the condition of the air over a large 
portion of the path. The soundings just described 
were made primarily for correlation with the signal 
strength measurements. 

The second plan was to obtain soundings in succes- 
sive steps in air moving off the coast as that air be- 
came more and more modified by the cool ocean sur- 
face. For this reason, days during which the air was 
westerly or nearly so were set aside for this type of 
measurement. The Duxbury soundings gave a rep- 
resentation of the structure of the air before it left 
the land. One airplane made soundings at about 2, 
7, and 25 miles offshore. The times of take-off were 
staggered to allow the first airplane to complete its 
third ascent before the second plane would begin its 
first sounding. 

The boat played a vital role in such a plan. It ran 
along the line of the air trajectory for as long as was 
practicable to take water temperature measurements 
and mast soundings, usually an 8- to 10-hour period. 

The Race Point Meteorological Station was coor- 
dinated into this general plan by having it take con- 
tinual balloon soundings at, say, 2-hour intervals 

“By I. Katz, Radiation Laboratory, Lt. J. R. Gerhardt, 
Lt. W. E. Gordon, Army Air Forces, and P. W. Kenworthy, 
U. S. Weather Bureau, Boston, Mass. 


both before and after the airplane ascents. The pur- 
pose of these soundings was both to fit in as an extra 
sounding in the general plan and also to yield some 
information as to amounts of change of the meteoro- 
logical conditions with time. Also, in general, the 
times of soundings at Race Point Station were sched- 
uled about 1 hour later than those at the overland 
station to give the air sufficient time to travel from 
one to the other. 

Forecast Program 

A forecast program was begun during July and 
continued to October 10, 1944, in order to try out 
existing methods of forecasting and to help develop 
new techniques. A more natural step would have been 
to analyze the data taken during the summer and 
then to put that analysis into the form of forecast 
procedures, as was done at the end of the 1943 Boston 
Harbor transmission experiment. However, since speed 
was essential it was decided to initiate a forecast pro- 
gram simultaneous with the observations. The very 
act of forecasting tended to focus attention on the 
important weather factors, at the same time giving 
invaluable help in planning the day-to-day observa- 
tions. 

The type of forecast made was different from the 
usual form. It consisted of a “space forecast’’ rather 
than the usual time forecast. That is, knowing the 
conditions at one point at a given time the problem 
was one of finding the conditions at another location 
at the same time. It involves the entire problem of 
modification of an air mass by a water surface. 

The forecasts were in the form of curves of tem- 
perature and moisture, from which the modified in- 
dex curve was computed. A time and a location in 
Massachusetts Bay were selected at which it had been 
determined previously that a sounding would be made. 
Almost invariably airplane observations were chosen 
to use as verifications because those soundings were 
at sufficient altitudes so that both the modified and 
the unmodified air were sampled. The forecasts were 
made from the surface to 1,000 ft, whereas the air- 
plane soundings started from about 20 ft and con- 
tinued to 1,000 ft. For verification, the forecast and 
the sounding were plotted on the same graph. 


107 


108 


METEOROLOGY— FORECASTING 


8.1.3 Army Analysis and Forecasts 

The program of the Army forecasters included the 
forecasting of transmission and radar ranges ; the ap- 
proach to this problem was empirical. The basis of the 
program was again the analysis of the first 6 weeks’ 
data, this time including the signal strength meas- 
urements which have been described. Signal strengths 
were divided into four ranges qualitatively described 
as low, standard, high, and very high, corresponding 
to M curves of the types substandard, standard, super- 
standard, and trapping. This analysis did not con- 
sider variations in the M curve over the path but 
rather related signal to the prevailing type of curve. On 
this basis, then, a transmission forecast for a 24-hour 
period involved the forecasting of prevailing M curves 
over the transmission path for appropriate time in- 
tervals. The length of these time intervals was deter- 
mined by the rapidity with which the weather factors 
affecting the M distribution were changing. Specific- 
ally, a 24-hour transmission forecast involved two 
4/-curve forecasts plus forecasts of temperature and 
dew point trends. These forecasts were supplemented 
frequently with iff -curve forecasts for times of mini- 
mum or maximum propagation conditions. These 
meteorological data could then be translated quali- 
tatively into values and trends of signal strength. This 
information was presented in the form of a graph of 
signal strength versus time. 

How the Forecast Is Made 

The forecast in general involves two determinations : 
one, of the initial conditions of the air before it leaves 
land; and two, the modifications of the air by the 
water surface. A study of the synoptic situation and 
the low-level circulation reveals the location of the 
point where the air in question leaves the land. The 
synoptic situation shows the general flow pattern; 
local winds from the surface to 2,000 ft indicate the 
specific pattern over the area under consideration. 

The initial temperature and moisture distributions 
are determined by studying the local hourly teletype 
sequences and radiosonde observations. The modifica- 
tion of the air is determined by considering the relation 
of the surface water temperature to the representa- 
tive air temperature and dew point, the over-water 
travel, and the rate of modification. 

Time forecasts were also made by the Army fore- 
casters. They involved straight meteorological fore- 
casts of the initial conditions to which were applied 
the space forecast technique just described. 


Example. This is a forecast made by the Weather 
Bureau. The synoptic weather map on the morning 
of July 26 indicated a rather weak flow of modified 
continental polar air moving in an easterly direction 
from the mainland of eastern Massachusetts out over 
the waters of Massachusetts Bay. The temperature of 
this air was potentially more than 21 C and under 
sunshine was developing surface temperatures near 
the shore line of more than 21 C by 0800. The fore- 
cast was for 1000 about 5 miles southeast of Eastern 
Point, Massachusetts. The temperature over land 
about a half-hour before this was expected to be about 
24 C, and the air flow as indicated by winds aloft was 
such as to allow the air warmed to about this figure 
to be out over this position within a half-hour. The 
lapse rate over land would be approaching the dry 
adiabatic by this time; so, as a guide, a lapse rate 
amounting to about 3 C per 1,000 ft was projected 
to 1,000 ft starting from 24 C at the surface. A value 
for the sea water temperature of 17 C was predicted 
from recent observations made in the Bay. Using past 
experience, one then assumed a water modification up 
to about 300 ft, and the T curve was constructed 
starting from the surface value of 17 C, showing a 
sharp inversion at first and a gradual inversion until 
it met the guiding line representing the air from the 
land. The radio observation made at MIT about mid- 
night, July 25 to 26, was considered to be a fairly 
good check of the properties of the air mass involved. 
A surface temperature of between 21 and 22 C was 
indicated. 

In forecasting the moisture curve, a value at the 
surface corresponding to the water temperature was 
made the base of the curve. Over-land dew points were 
initially predicted to be about 13.5 C, which would 
give a vapor pressure value of between 15 and 16 mb 
at the top of the water modification zone. An examina- 
tion of the raobs, both MIT and Portland, show mix- 
ing ratios of about 10.5 g per kg between 500 and 
1,000 ft, which corresponds to 15 or 16 mb. This makes 
a good check on the prevailing initial dew points. The 
raob at Albany indicated that air which was a little 
drier was moving in from the west so that a slight 
decrease in the vapor pressure was forecast between 500 
and 1,000 ft. (This part of the forecast did not prove 
to be correct, since, as the verification of the forecast 
in the figure shows, the moisture value remained 
fairly uniform from 400 up to 1,000 ft.) Another 
curve was drawn similar to the T curve to connect 
the surface vapor pressure value with that value at 


RADAR PROPAGATION FORECASTING 


109 


the top of the water modification zone, and from 
there to 1,000 ft a gradual decrease was forecast on 
the basis of the conclusions regarding the advection 
of a little dry air indicated by the midnight Albany 
sounding. 

The verification shown by the broken line in Fig- 
ure 1 turned out rather well in this instance. The 
computed and verified M curve proved to possess 
almost identical slopes throughout with the top of 

FORECAST 

VERIFICATION 

JULY 26,1944 lOOOE WEATHER BUREAU FORECAST 27 
SMILES SOUTHEAST OF EASTERN POINT, MASS. C77 


17 19 21 23 14 16 18 20 -20 -10 0 10 20 

TEMPERATURE VAPOR PRESSURE M -Mq 

IN C IN MILLIBARS 

Figure 1. Space forecast of M curves. 

the M inversion in both very close to 150 ft. This was 
one of the better forecasts. It can be seen that actual 
values of temperature and vapor pressure between 
forecast and verification might vary by several de- 
grees, but as long as they have the same slopes at the 
same elevation they will produce M curves reason- 
ably close to one another. 

Conclusions. It is felt that the method of forecast- 
ing used was a marked improvement over the tech- 
nique employed previously. It is potentially capable 
of dealing with the low-level modification problem 
in the case where the intial air is stratified as well as 
the one in which the initial air is homogeneous before 
it passes out to sea. 

8 2 RADAR PROPAGATION FORECASTING‘S 

This is a report of results obtained by an AAF 
board project investigating radar propagation fore- 
casting, which was started as two distinct programs in 
September 1944. The first part of the project was 
carried out at the Radiation Laboratory with facili- 
ties used by Group 42 during over-water transmission 
measurements in the summer of that year. During 
that time, with the invaluable assistance of Group 42, 
a forecasting system was developed for the over-water 
case, the results of which are presented in Section 

^By Lt. J. R. Gerhardt and Lt. W. E. Gordon, AAF Board. 


8.1.® These reports gave preliminary results of the 
MIT program and the recommended forecasting pro- 
cedures. The second part of the propagation forecast- 
ing program was set up at Orlando, Florida, to study 
particularly the over-land forecasting phase and to 
investigate some of the operational uses of such fore- 
casts. 

With this in mind, AAF Board Project H3767, 
^‘^The Determination of the Practicability of Forecast- 
ing Meteorological Effects on Radar Propagation,^’ 
was initiated late in 1945 with the following specific 
objectives : 

1. To determine the practicability of forecasting 
those low-level meteorological conditions which affect 
radar propagation. 

2. To determine the accuracy with which radar 
propagation forecasts can be made from the corre- 
sponding meteorological conditions. 

3. To determine the operational uses of such fore- 
casts. 

4. To determine the optimum meteorological ob- 
servation site with relation to the site of the radar 
employing the forecasts. 

5. To determine the suitability of available low- 
level sounding equipment. 

It was originally planned to study the over-land 
and over-water problems simultaneously, but because 
of the lack of a coastal radar site until the last month 
of the program the project was divided into two 
phases: (I) the general study of the over-land prop- 
agation variations in an attempt to devise a suitable 
forecasting procedure and (2) an evaluation of the 
results obtained from both the over- water and over-land 
methods, with possible tactical applications under field 
conditions at the site of a powerful coastal radar. 

Figure 2 is a map of central Florida giving in de- 
tail specific facilities used throughout the project. 
Headquarters was established at the Weather Central, 
Orlando, where complete weather information, fore- 
casts, and analyses were available. The meteorological 
data used throughout the project consisted of surface 
and upper air observations for the general central 
Florida area. 

Detailed synoptic maps of Florida were drawn cov- 
ering periods of 6 hours each to determine wind 
patterns and representative land temperatures and 
dew points ; piballs^ for Orlando, Sebring, and Tampa 
were plotted up to 2,000 ft to determine trajectories and 

- “Elaborated in references 1 to 3. 

‘‘A small balloon with standard rate of rise released for 
tracking by a theodolite for estimation of upper-air winds. 




110 


METEOROLOGY— FORECASTING 



Figure 2. Map of central Florida with locations of weather and radar installations used in Project 3767. 


wind speeds above surface levels, while the Orlando, 
Tampa, Tallahassee, and Jacksonville raobs were 
studied to correlate subsidence and radiation effects 
with radar propagation variations. 

During the first phase of the project, sounding sta- 


tions were established at Leesburg and New Port 
Richey using both the Washington State College 
wired sonde and the MIT psychrograph. Radar data 
were taken from the S-band V beam and the P-band 
SCR-588 at Tomato Hill, only a few miles from the 


RADAR PROPAGATION FORECASTING 


111 


Leesburg sounding site, the SCR-584 at Winter Gar- 
den, and the P-band SCR-271 at Crystal River dur- 
ing their operating hours. The Tarpon Springs pro- 
gram employed a medium early warning and an SCR- 
615 radar, both on S band, located on the Gulf coast, 
and the Crystal River SCR-271 and Winter Garden 
SCR-584. The sounding station was located within 
a half mile of the Tarpon Springs radar site. During 
the entire program sea surface temperatures were 
measured several times weekly at either the Cedar 
Iveys or Anclote Crash Boat bases out to a distance 
of about 20 miles at 2- to 4-mile intervals. 

Low-level soundings were made during the entire 
project primarily as an aid in interpreting radar per- 
formance and in determining representative air values 
and secondarily in an attempt to evaluate the opera- 
tional suitability of the available sounding equip- 
ment. Results of the latter portion of the work will 
be presented later in this report. Ground-based sound- 
ings were made by means of various combinations of 
350- and 700-g balloons, 7-ft Seyfang kites, and a 
small barrage balloon. 

The sounding stations were originally located so 
as to be as representative as possible of interior and 
coastal areas, although it was found later that, with- 
out the additional mobility of airborne measurements, 
individual ground-based soundings were likely to be 
too strongly influenced by local topographic effects to 
be completely reliable. Because of clearance require- 
ments, the ground-based soundings were restricted to 
600 ft, although it was determined that 1,000 ft would 
be a much safer limit, with occasional measurements 
up to 3,000 ft considered desirable. Soundings were 
taken before dawn at 1000 Eastern War Time, after 
sunset, and at 2300 EWT to obtain sufficient data on 
the effects of radiation and other meteorological phe- 
nomena. As far as speciflc sounding procedures are 
concerned, both the small balloons and kites gave 
satisfactory results, although for most of the wind 
speeds encountered in this area the 7-ft kite was too 
small for efficient operation. No limiting surface wind 
speed can be given as a dividing line between kite and 
balloon operation, since it has been found that occa- 
sionally even in surface calms strong velocity gradi- 
ents exist immediately above the surface layer. Al- 
though it is realized that a barrage balloon is not a 
standard item of equipment for sounding measure- 
ments, it is unreservedly recommended and whenever 
available should he used for simplicity and relia- 
bility of sounding procedure. 


The method employed in this project for the 
radar verification of superrefraction was to record 
ylan position indicator [PPI] scope appearance of 
ground clutter return. The oscilloscope screen was 
assumed segmented into eight 45° sectors, and the 
maximum range on a ground target in each sector was 
noted hourly during periods of operation. In an at- 
tempt at correlating the radar performance with the 
existing meteorological conditions, a classification 
system was devised in which each distinguishable 
propagation condition was assigned a single number. 
After collecting observations for some time from each 
unit the data were examined, and an average of the 
normal pattern was chosen as the standard, or class 
1, type of propagation. Averages of reported increased 
ranges in various sectors were calculated, while the 
azimuthal variations due to shadow effects of sur- 
rounding terrain, coast line and obstructions were 
considered. The consistency with which various in- 
creased range averages were attained determined the 
number of classes of propagation assumed for each 
unit. On the assumption that the meteorologist could 
forecast and correlate iif -curve types corresponding 
with four types of propagation, four such propaga- 
tion classes were chosen for the S-band V beam and 
the P-band SCR-271 at Crystal River. Figures 3 and 
4 show the four classes of propagation as defined for 
the SCR-271 at Crystal River. The class 4 picture 
deflnitely shows the Florida coast-line detail painted 
in. Observations from most of the other units, how- 
ever, were classed only as 1 (standard) and 2 (non- 
standard) propagation because of the radar shadows 
of certain topographical features near their sites. Due 
possibly to the peninsular situation of Florida, it was 
impracticable to forecast accurately four different 
classes of propagation, but forecasting on a basis of 
two classes, standard and nonstandard, can and 
should be done. 

During the first part of the over-land program an 
attempt was made to forecast the specific M curves 
as shown by the Leesburg and New Port Richey 
sounding stations and to correlate these curves with 
the two to four propagation classes outlined for each 
radar unit. However, because of the wide variation 
of surface terrain (sand, swamps, lakes, forests) in 
this general area, no single sounding was necessarily 
representative of the entire air mass, since subsid- 
ence and radiation effects almost certainly varied con- 
siderably over the different kinds of terrain surround- 
ing the sounding locations. On this basis, then, rather 


112 


METEOROLOGY— FORECASTING 


than attempting to forecast a hypothetical representa- 
tive M curve, a series of correlations was made relat- 
ing the general synoptic situation directly to the radar 
performance. Using this method, the actual over- 
land forecasting results showed that, while approxi- 
mately 80 to 85 per cent of the total operating hours 
could be correctly forecast as either standard or non- 
standard propogation periods, only some 50 per cent 
of the nonstandard hours could be forecast correctly. 
This is only a little better than climatology, and 
more work remains to be done on the over-land fore- 
casts of propagation variations. 

In addition to the ground clutter verification of 
superrefraction, several low-level coverage flights were 
made from Leesburg to Crystal River and some 80 
miles out into the Gulf at an altitude of 100 ft, ret- 
turning at 1,000 ft to check coverage above duct levels. 
Only a very few flights were made during periods of 
extended propagation, but during these periods, while 
interference from extended ground clutter prevented 
detection of the plane over land, extended ranges were 
recorded for the VHF (very high frequency) air-to- 
ground communication contact. 

In a further attempt to investigate some of the 
operational possibilities of trapping conditions at low 
and intermediate altitudes, measurements were taken 
of maximum ranges on the airborne X-band APQ/13 
radar during routine flights. However, as the ranges 
observed were very erratic, no conclusions could be 
drawn. In this respect it should be stated that while 
excellent cooperation was obtained in getting various 
radar and aircraft observations, the project had a 
low priority and as a consequence could not fully in- 
vestigate many of the more important operational 
possibilities which would have required extensive use 
of radar and aircraft facilities. 

The over-water forecasting program at Tarpon 
Springs was set up to compare the results of fore- 
casts made under field conditions of limited meteoro- 
logical data with those made using all available mete- 
orological information given in the forecasting sys- 
tem presented in reference 3. This system was based 
primarily on the over-water modification studies 
presented at the last conference, where duct height d 
was related to the wind speed at 1,000 ft, the distance 
of over-water travel, and the M deficit, which is the 
difference between the M value at some reference level, 
in this case the sea surface, and the M value of the 
unmodified air reduced to sea level. In general, no 
attempt was made to forecast the specific lapse rates 



Figure 3 A. Typical Class 1 pattern, P-band SCR-271, 
Crystal River. Grid squares are approximately 5 miles 
on a side. 



Figure 3B. Typical Class 2 pattern, P-band SCR-271, 
Crystal River. 


and M curves corresponding to the current meteoro- 
logical situation. With uniform weather conditions 
existing over water, there was assumed a 100 per cent 
correlation betwen the M curve and the corresponding 
radar performance, so that it was merely necessary 
to determine the representative d and AiR of the air 
mass to obtain the complete propagation forecast. 





RADAR PROPAGATION FORECASTING 


113 



Figure 4A. Class 3 pattern, SCR-271, Crystal River. 
Coast line well painted in. 


Figure 4B. Typical Class 4 pattern, SCR-271, Crystal 
River 

As it was impracticable to establish a permanent 
target in the Gulf of Mexico beyond the radar hori- 
zon, the existence of superrefraction was generally 
assumed when there was extended appearance of 
coast-line clutter. It is realized that such an effect 
may not be representative of open water conditions 
because of the possibility of local sea breezes giving 


rise to the necessary temperature and moisture gradi- 
ents for trapping. However, on this basis, 18 out of 
30 forecasts correctly verified the presence or absence 
of extended coast-line clutter to within 1 to 3 hours 
of the total duration. With extended echoes existing 
during 55 per cent of the test days over the coastline, 
this accuracy is considerably greater than could be 
arrived at by any purely statistical procedure. It 
should be stated here that these forecasts proved to 
be particularly valuable to the radar personnel, since 
certain engineering tests in progress on the radars 
made an accurate evaluation of the effects of super- 
refraction on the radar set performance necessary 
during the calibration flights. 

As an additional check on the existence of super- 
refraction over water, forecasts were made of the 
ranges for S-band radars and VHF communication 
on low-level coverage flights into the Gulf. Of a total 
of ten flights, six were made during periods of ex- 
tended coast-line return, three of which were cor- 
rectly forecast as giving superrefraction on S-band 
radar and two as giving increased ranges on VHF 
communication. Although this is not so accurate as 
the forecast of surface effects, a large error may have 
been introduced by the fact that the forecasted duct 
heights were of the same order of magnitude as the 
lowest levels attained by the plane in its flight over 
the Gulf. All the over-water flights showed normal 
horizon ranges at 1,000- to 3,000-ft levels on the re- 
turn legs. 

In another attempt to determine the vertical cov- 
erage patterns resulting from low-level nonstandard 
propagation, several free balloon flights were made. 
Standard weather service reflectors were attached to 
the balloons, which were released from Army crash 
boats at distances of 30 and 60 miles from the coast. 
Possibly because of lack of radar efficiency, only the 
balloons released at 30 miles were picked up by the 
coastal radar. Although no nonstandard conditions 
were observed during the releases, the method seems 
suitable for making vertical coverage measurements. 

Eadar and weather data for the period January 1 
to March 15 were tabulated and analyzed during the 
month of March. The primary data consisted of S- 
band radar reports from Winter Garden and Lees- 
burg and low-level soundings from Leesburg, sup- 
plemented by the synoptic charts and radiosonde ob- 
servations supplied by the 36th Weather Region. 

The analysis resulted not in a system of forecasting 
such as that developed for over-water use but rather 






114 


METEOROLOGY— FORECASTING 


in a series of clues to be used as an aid to over-laud 
forecasting in Florida* Since the clues are closely 
related to the topography and peninsular situation 
of Florida and to the season of the year, they are not 
directly applicable to other locations in their present 
form. However, they suggest that investigation of 
these points at other locations would quickly yield 
useful correlations. Some examples of these relations 
follow. 

1. Of the 600 ft low-level sounding standard curves, 
90 per cent gave standard ranges. 

2. During early morning hours: 

a. Surface winds of 10 mph or more produced 
standard propagation always; winds of 5 to 9 
mph produced superrefraction 20 per cent of 
the time ; 2 to 4 mph showed superrefraction 
60 per cent of the time ; and calm winds pro- 
duced superrefraction almost always. 

b. Similarly, the 1,000-ft winds of 30 mph or 
more produced standard, while 1,000-ft winds 
of 10 mph or less almost always produced 
superrefraction. 

c. Superrefraction occurred with clear skies ex- 
cept on two occasions, one with broken high 
clouds, the other with broken middle clouds, 
never with low clouds. 

d. High-pressure centers within 7 00 miles and with 
gradients of 1 mb per 100 miles or less pro- 
duced superrefraction. 

e. Ground fog patches were observed during pe- 
riods of class 4 propagation, with two excep- 
tions. 

3. Simple surface ducts of 70 ft and Ad/go (refer- 
ence level 50 ft) of 4 or more and elevated S curves 
with ducts above 200 ft and Ail/gg of 6 or more pro- 
duced class 3 or 4 propagation with possibly one ex- 
ception. 

4. Large Ad/’s observed by radiosonde between 
1,000 and 3,000 ft showed no correlation with S-band 
propagation but did show fair correlation with super- 
refraction on P band. Superrefraction on both S and 
P band showed good correlation with large Al/’s ob- 
served below 1,000 ft. 

5. The height of the temperature inversion in- 
creased with increasing 1,000 ft wind speeds up to 
10 or 12 mph, then decreased slowly with further in- 
crease in wind. 

6. Substandard propagation conditions were never 
observed over land, either on the radar or the sound- 
ings. 


A series of low-level soimdings taken at hourly in- 
tervals throughout the night were related to corre- 
sponding radar ranges. The soundings were made at 
Leesburg; the radar data were taken at Tomato Hill 
(2 miles west of the sounding site) and at Winter 
Garden (25 miles southeast of the sounding site). 

The general weather situation for the night of 
March 5 to 6 shows maritime tropical air pouring up 
over Florida around the western end of the Bermuda 
high, giving clear skies and southerly winds of 10 mph 
at 1,000 ft and 2,000 ft at 2000 EWT,® increasing to 
20 and 25 mph respectively by midnight, and to 23 
and 35 mph by 0400. Figure 5 shows the PPI scopes 


Figure 5. SCR-588, Leesburg, night of March 5 to 6, 

1945. 

of the P-band SCR-588. The arrows point north; the 
small grid squares are 5 miles on a side. Before mid- 
night, propagation was standard, as illustrated by the 
0400 frame. The ranges built up rapidly, reaching 65 
miles and decreased slowly between midnight and 
0400. (Radar shadows of surrounding topographical 
features account for the uneven distribution of range 
increase.) 

Figure 6 shows the progression on the S-band SCR- 
584. The bold line points north, the range markers are 
at 10,000-yd intervals. (The sounding site is roughly 
315° at 45,000 yd.) From 1900 to 2200 propagation 

®All times to follow are Eastern War Time. 




0030 EWT 


0300 EWT 


0130 EWT 


0400 EWT 


RADAR PROPAGATION FORECASTING 


115 



0400 EWT 


Figure 6. SCR-584, Winter Garden, night of March 5 
to 6, 1945. Superstandard propagation occurs to the 
northwest at 0100 and 0300 EWT. At 0400 EWT the 
pattern is again standard. The line on the PPI indicates 
true north. 

went from standard to above standard and returned to 
standard. After midnight ranges built up rapidly and 
held until after 0300, when they began a gradual re- 
turn to standard, reaching that condition shortly after 
0400. 


The M curve measured at 1900 was standard, fol- 
lowed by those illustrated in Figure 7. Unfortunately, 
no soundings weit taken between 2035 and 0008, and 
consequently the evolution of the elevated S from the 
surface duct is not shown. We know that the surface 
wind decreased from 4 mph at 2000 to calm at mid- 
night, while the 1,000-ft wind increased from 10 to 
20 mph. The duct height and Ad/ value were approxi- 
mately constant from midnight to 0200, after which 
the curve gradually approached standard. 



o i I > I l_£J 

350 355 360 365 370 355 360 365 370 355 360 365 370 




355 360 365 370 355 360 365 370 360 365 370 375 380 
0205 EWT 0315 EWT 0402 EWT 

Figure 7. M curves for night of March 5 to 6, 1945, 
based on soundings at Leesburg AAF. 


Table 1 summarizes the weather and radar varia- 
tions. It should be pointed out that the antenna height 
for the P-hand SCR-588 was 140 ft above the sound- 
ing site, for the S-band SCE-584 the same height as 
the sounding site. Thus at 2100 we have a 200-ft sur- 
face duct trapping the SCR-584, but not trapping the 


Table 1. Radar-weather tabulation, March 5-6. 



19 

20 

21 

22 

23 

Time (EWT) 

00 01 02 

03 

04 

05 

06 

07 

SCR-584 ground range* (S-band) 

1 

2 

2 

1 

1 

1 

2 

2 

2 

1 

1 

1 

1 

SCR-588 ground range (P-band) 

, , 

. , 

1 

• • 

• , 

2 

2 

3 

2 

1 

1 

1 

1 

Af-curve typef 

S 

D 

D 

, , 


L 

G 

L 

L 

S 

Ta 

S 

S 

Duct height (ft) 


200 

200 

, , 


370 

350 

380 

400 


450 



AM 


14 

14 



14 

14 

14 

11 


6 



Surface wind (mph) 

5 

4 

4 



0 

1 

3 

5 

6 

6 

5 

7 


♦Ground range: 1, standard; 2, 3, 4, degrees of superrefraction. 

tAf -curve types: S, standard; D, duct (simple surface trapping); G, ground-based S curve; L, elevated S curve; T^, transitional aloft. 



116 


METEOROLOGY— FORECASTING 


SCE-588 (duct height 60 ft above the antenna), while 
from midnight to 0300 an elevated duct of the order 
of 380 ft traps both sets (duct height some 250 ft 
above the SCR-588 antenna). By 0400 the winds 
became strong enough to wipe out the stratified layers 
and mix the air, giving standard conditions. At 0500 
a trace of a transitional condition aloft appears in the 
sounding but is not sufficient to extend the range. 

During the months of January and February data 
were collected on S-band V beam at Tomato Hill 
during 47 days. Of these days^ observations 37 per cent 
showed nonstandard conditions. During the same pe- 
riod the SCE-271 at Crystal Eiver show^ed at least 
slight increases in ranges on 72 per cent of the days’ 
observations which were recorded, although oidy 17 
per cent attained the strength of class 3. 

1’he longest ground range observed on the S-band 
set at Tomato Hill was 200 miles on the morning of 
January 25, while the longest ground range observed 
on the SCE-271 at Crystal Eiver was 140 miles on the 
morning of February 17. Both these ranges were the 
maximum permitted by the radar presentation. 

During the month of April at Tarpon Springs, 65 
per cent of 24 days’ observations showed nonstandard 
conditions, with 46 per cent giving surface return at 
greater than 80 miles, indicating strong superrefrac- 
tion. The longest range recorded was the coast-line 
effect out to 220 miles. 

To determine suitable low-level airborne sounding 
equipment, the psychrometer equipment ML-313/AM, 
the WSC wired sonde, and sling psychrometer ML- 
24A were mounted in aircraft L-4 (cruising speed 55 
mph) and compared with the MIT psychrograph car- 
ried by a barrage balloon. 

From considerations of the forecasting method an 
accuracy of ±0.2 C in wet and dry bulb temperatures 
and a lag coefficient less than 45 sec are desirable. The 
accuracy of the MIT psychrograph is ±0.2 C in tem- 
peratures, with a lag coefficient of the order of 15 sec. 

These data were gathered during hours of daylight 
and are spread rather evenly between 0900 and 1700. 
The MIT psychrograph was held at a fixed point in 
space where a conservative estimate of the fluctuations 
of temperature was 0.3 C. The airborne instruments 
integrate the measurements for a given level, hence a 
spread in the data is reasonably indicated and the 
statistical value of sigma may be considered represen- 
tative of the accuracy of the test instrument. 

The procedure for each test instrument involved 
making five to ten regular low-level soundings supple- 


mented by a series of passes at a fixed level. Necessary 
ground checks were carefully made using forced ven- 
tilation, and standard corrections for airborne instru- 
ments were applied. 

Psychrometer equipment ML-313/AM, consisting 
of a wet and dry bulb thermometer in a streamline 
housing, was mounted as far back in the cabin of the 
L-4 as was practical. Since the L-4 is a single engine 
plane it was expected that the engine heat and propel- 
ler blast would influence the readings. The data are 
as follows : 


Dry bulb 

Number of pairs of readings: 174 

Average difference: — 0.06 C 

07% of the points agree to within 0.20 C 

Wet bulb 

Number of pairs of readings: 156 

Average difference: + 0.08 C 

67% of the points agree to within 0.14 C 


The ML-313 was, in addition, mounted on aircraft 
L-5 (single-engined, cruising speed 100 mph). The 
data are similar to those given above. The data indicate 
that, despite the expected influences of propeller blast 
and engine heat, the equipment is suitable for low- 
level soundings for propagation work. 


DRY BULB TEMPERATURE 




DIFFERENCE EQUALS MIT PSYCHROGRAPH LESS 
ML 313 IN DEGREES CENTIGRADE 

Figure 8. Instrument comparison, MIT psychrograph 
and psychrometer ML 313/AM on Aircraft L-4. 


RADAR PROPAGATION FORECASTING 


117 


NUMBER OF POINTS 140 
AVERAGE DIFFERENCE +0.10 
MEDIAN +0.1 

MODE -0.1 

O' 0.30 C 


DRY BULB TEMPERATURE 



VAPOR PRESSURE 



DIFFERENCE EQUALS MIT PSYCHROGRAPH LESS WSC WIRED SONDE IN DEGREES CENTIGRADE 
AND MILLIBARS OF VAPOR PRESSURE 

Figure 9. Instruincnt coniiiarison. MIT i)syclirogiai)h and M'SC wired sonde on Aireraft L-4. 


The WSC wired sonde was mounted on the strut 
of the L-4 some 5 ft away from the cabin of the 
})lane. The comparison data follow: 


Dry bulb 

Number of pairs of readings: ' 140 

Average difference: + 0.10 C 

67% of the points agree to within 0.30 C 

Vapor pressure 

Number of pairs of readings: 140 

Average difference: + 0.06 mb 

67% of the points agree to within 0.98 mb 


The differences in moisture readings are rather 
larger than desirable. 

The sling psychrometer ML-24A was tested sim- 
ilarly but was considered unsuitable because of lack of 
protection from radiation. 

Of the ground-based sounding equipment used dur- 
ing the program, the MIT psychrograph consistently 
gave excellent results. The WSC wired sonde is capable 
of good results, but several mechanical difficulties 
render it unsuitable for field use by the services in its 


present form. It is expected that these difficulties will 
be ironed out in a revision of the wired sonde. 

The following statements are the personal opinions 
of the authors and do not represent the official opinion 
of the Army Air Forces Board. 

1. There is a military need for a propagation fore- 
casting service. If a radar set is to be used most effi- 
ciently, its full capabilities and limitations (including 
the effects of weather) must be known. 

2. Propagation forecasts over water using the 
method described in reference 3 are sufficiently 
accurate for operational purposes. It is recommended 
that further experimental study of long over- water 
propagation and vertical coverage be carried on. 

3. Propagation forecasts over land are not suffi- 
ciently accurate for operation uses. Further study of 
the over-land forecasting problem is indicated. 

4. For maximum operational employment of the 
forecasts, the forecaster should be located at the radar 
site. Communication with a class A weather station, 
a ground-based low-level sounding station at the radar 



118 


METEOROLOGY— FORECASTING 


site, and supplementary airborne soundings are re- 
quired. 

5. Psyclirometer equipment ML-313/AM mounted 
on a slow, single-engined aircraft is suitable for low- 
level airborne soundings for propagation forecasting 
work. 

8 3 APPLICATION OF FORECASTING 
TECHNIQUES AND CLIMATOLOGY ^ 

Introduction 

PuurOSES OF THE RePORT 

1. To make available, primarily to radar and mete- 
orological officers, information on the principal mete- 
orological factors which have an important effect on 
radio and radar performance. 

2. To indicate how suitable utilization of certain 
of these meteorological factors can lead to improved 
efficiency and increased exploitation of radio and 
radar devices: 

a. With respect to variable adjustments applied 
to daily routine operations (such as the sup- 
plementary use of scouting ^Dianes when the 
coverage of early warning radars is anticipated 
to be poor, etc. ) . 

b. With respect to longer-range planning in es- 
tablishing radio and radar stations (optimum 
choice of sites, most desirable frequencies to 
use, etc.). 

Material Covered in the Report 

Badio-Meteorology. Since most of the basic infor- 
mation which has been obtained by various research 
groups and in military and naval operations involving 
radar is familiar to the reader or is adequately covered 
in other reports,^''^ the essential points with reference 
to the effect of meteorological factors have been ex- 
tracted and are here presented in condensed form. The 
primary emphasis is on the phenomena associated with 
nonstandard propagation, i.e., on the conditions under 
which radar ranges are unusually large or unusually 
small. Related elements — temperature, humidity, the 
variation of each of these with height, M curves, 
ducts, etc. — are defined, and the role they play in the 
effectiveness of radar performance is discussed briefly. 

Specific Relationships between Meteorological Ele- 
ments and Radar Performance. Of the several investi- 

^By A. T. Waterman, Jr., and C. Harrison Dwight, Colum- 
bia University Wave Propagation Group. 


gations carried out on this subject, mostly in connec- 
tion with the prediction of trapping effects and conse- 
quently of radar ranges, one which has met with as 
much success as any and is fairly similar in essence 
to some of the others is presented here. It was devel- 
oped in a study of the modification that air undergoes 
in passing over water and is designed to predict the 
formation and subsequent structure of surface ducts 
which are formed along coast lines and over oceanic 
areas. 

From observations of the representative surface 
temperature and humidity of the air, the sea tempera- 
ture, and the wind direction and velocity, this method 
indicates whether a surface duct is to be expected and 
the height to which it is likely to extend. Practical 
application of the method can therefore be of direct 
assistance in anticipating radar performance for short 
periods in advance or for regions where detailed mete- 
orological observations may be limited. Enough par- 
ticulars, together with charts and nomograms, are 
given to enable one with meteorological training to 
apply these prediction techniques and thus facilitate 
daily or hourly adjustments to make optimum use of 
radar equipment. 

Computed Climatological Information on Surface 
Ducts. To obtain a broad picture of the variation in 
radio and radar ranges likely to be encountered in the 
western Pacific region, average duct widths (height 
from the base to the top of the duct) have been com- 
puted. These computations are based on the relation- 
ships between meteorological elements and radar per- 
formance mentioned above and utilize climatological 
data consisting of monthly averages of air tempera- 
ture, humidity and sea temperature, and monthly 
frequencies of winds with specified direction and 
speed. 

The area covered includes the Japanese islands, the 
coasts of Korea, Manchuria, and China, the northern 
Philippines, the Marianas, the Bonins, and the Ryukyu 
Islands — approximately 10°to50°N latitude and 120° 
to 150° E longitude. The computations indicate the 
percentage of time surface ducts of various widths may 
be expected at different times of the year and at dif- 
ferent locations within the region. This information is 
summarized in tabular form. The results are not in- 
tended to represent an accurately detailed picture but 
do give a sufficiently close approximation of average 
conditions influencing certain aspects of radio and 
radar performance so that they may be used as a 
guide in long-term operational planning. 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


119 


Radio-Meteorology 

Evidences of Nonstandard Profagation 

Since the start of the war, cases of very long radio 
ranges and radar coverages, together with extreme 
variations of these quantities, have become well known 
to personnel working at microwave frequencies. Such 
phenomena, when due to influences acting on the 
propagated electromagnetic waves and not to freak 
behavior in set performance, have been classed under 
the term nonstandard propagation. It has been found 
that nonstandard propagation (such as is illustrated 
by the behavior of microwaves when they are con- 
strained to follow a path of such curvature that the 
rays remain close to the surface of the earth and hence 
reach otherwise inaccessible targets — a phenomenon 
frequently referred to as trapping) is directly associ- 
ated with certain conditions that occur in the lower 
levels of the atmosphere (normally below 5,000 ft) 
which have been given the name of ducts. Detailed 
analyses of the structure of ducts have been presented 
adequately in the previously mentioned reports. Hence 
the paragraphs immediately following give only a brief 
and somewhat simplified description of the meteor- 
ological elements associated with ducts. 

Meteorological Conditions Associated 
WITH Ducts 

RemarJcs on Pressure, Temperature, and Humidity. 
The meteorological situations in which trapping of 
microwaves occurs involve certain types of stratifica- 
tion in the lower levels of the atmosphere. The amount 
of stratification is dependent on tlie vertical distribu- 
tions of pressure, temperature, and humidity. 

Although the atmospheric pressure at any particular 
elevation and, to a lesser extent, the rate at which 
pressure decreases with altitude may vary from one 
time to another, these variations are relatively unim- 
portant as far as their direct influence on propagation 
is concerned and so may be neglected in practical 
considerations. 

On the other hand, temperature and its change with 
altitude do have an immediate bearing on duct forma- 
tion. Under more or less average conditions through- 
out the troposphere, the temperature decreases with 
increasing altitude and the term ‘^Temperature lapse 
rate” is defined as the rate of decrease of temperature 
with height (and consequently is usually expressed in 
degrees Fahrenheit per 1,000 ft or degrees centigrade 
per kilometer). For reference purposes a ‘Standard” 
lapse rate has been taken as 3.47 F per 1,000 ft. 


(Further details of the National x\dvisory Committee 
on Aeronautics standard atmosphere are given in 
the Appendix on iiage 130.) Under certain conditions 
the temperature throughout a layer of the atmosphere 
may increase with height, in which case a temperature 
inversion (Figure 10) is Said to exist. 



Figure 10, Vertical variation of temperature showing 
a ground inversion EF and an elevated inversion BC. 

The slopes of the portions FG, AB, and CD denote 
standard conditions, a decrease of temperature with 
elevation. 

In general the lapse rate of temperature is im- 
portant in meteorology because of its relationship to 
the vertical stability of the atmosphere, that is, to the 
feasibility with which vertical air currents can de- 
velop. It turns out that, except within clouds or regions 
of active precipitation, the stability conditions can be 
closely evaluated from a knowledge of the actual lapse 
rate relative to the ‘Mry adiabatic” lapse rate (approxi- 
mately 5.5 F per 1,000 ft) . If the actual lapse rate is 
larger than the dry adiabatic, i.e., if the temperature 
decreases at a rate greater than 5.5 F per 1,000 ft in 
elevation, any vertical currents which develop will 
tend to exaggerate in intensity, and a condition of 
unstable equilibrium (Figure llA) will exist. Con- 
versely, if the actual lapse rate is less than the dry 
adiabatic or, especially, if a temperature inversion is 
present, the development of vertical currents will be 
hindered and the air will tend to become horizontally 
stratified. This is the case of stable equilibrium (Fig- 
ure IIC). The in-between case, in which the actual 
temperature lapse rate is the same as the dry adiabatic, 
is that of neutral equilibrium ( Figure IIB). 


120 


METEOROLOGY— FORECASTING 



Figure 11 . Temperature-height curves for the cases of 
(A) unstable air, (B) neutral air, and (C) stable air. The 
dry adiabatic (lapse rate) is indicated for comparison. 


Ill addition to the direct relationship which these 
stability conditions bear toward the trapping of 
microwaves, which will be described presently, there is 
also an indirect relationship caused by the modifica- 
tion that air undergoes when it moves over a sea or 
land surface with properties (temperature and mois- 
ture) different from those of the air itself. For ex- 
ample, air moving over land, the temperature of which 
is higher than that of the air, will be heated in its 
lowest layers by contact with the ground and thus 
tend to become unstable. This leads to vertical cur- 
rents which will carry the modifying influences to 
appreciable heights in the air. On the other hand, air 
moving over a surface cool in relation to the air will 
be cooled by contact with the ground, tend to develop 
stable characteristics, damp out vertical currents, and 
so confine the modifying influences to very low layers. 

The distribution of moisture with altitude, in its 
direct influence on nonstandard propagation, has an 
even more pronounced effect than that of temperature. 
As a means of describing the moisture content of the 
air, any one of several concepts may be used: dew 
point, wet bulb temperature, relative humidity, ab- 
solute humidity, specific humidity, and mixing ratio, 
all of which are defined in the Appendix. Except when 
evaporation or condensation is taking place (as in the 
case of clouds, rain, dew, etc.), the moisture content 
of the air has little effect on the temperature structure 
and therefore is not a major influence on stability 
conditions in so far as they are connected with the for- 
mation of ducts. What is of direct importance is the 
vertical distribution of humidity itself and the man- 
ner in which this distribution is affected by modifying 
influences. As an example of the latter, the case of 


warm and relatively dry air moving over a humid 
surface, such as dense vegetation or the ocean, might 
be mentioned. In this case, evaporation of water into 
the lower layers of the air leads to a greater decrease 
in moisture with altitude than was originally present 
in the air. 

Other modifying influences, of course, affect both the 
vertical distribution of temperature and humidity and 
the stability conditions of the air. Some of these are 
subsidence (the gradual sinking of large layers of 
air leading to increased stability and decreased rela- 
tive moisture content), radiation, and turbulent mix- 
ing. These are merely mentioned here in view of the 
fact that their various interactions at times may be- 
come quite complicated, hence requiring that proper 
interpretation be made by one trained or experienced 
in meteorology. 

Refractive Index. The manner in which pressure, 
temperature, and humidity directly influence trapping 
depends on the phenomenon of refraction or the bend- 
ing of rays as they pass through media with different 
dielectric properties or through a medium with vari- 
able dielectric properties. The velocity of electromag- 
netic waves through any particular medium such as 
the air depends on a quantity known as the refractive 
index of that medium. When the refractive index 
varies throughout the medium, as is usually the case 
in the atmosphere, the resulting variation in wave 
velocity leads to a bending of the rays. For example, 
the refractive index of the atmosphere often decreases 
with height, in which case rays are bent downward 
toward the surface of the earth, so that instead of 
traveling in straight lines they tend to follow to a cer- 
tain extent the curvature of the earth. The amount 
of bending depends on the manner in which the refrac- 
tive index varies with height. Under the proper con- 
ditions it is possible for rays to be bent to such a de- 
gree that they are confined to one layer of the atmos- 
phere. This phenomenon, the trapping of radio waves, 
is usually associated with only the microwave fre- 
quencies and is limited to those rays which leave the 
transmitter at an angle with the horizontal of less than 
1 degree, and therefore to only the lowest lobe in a 
radar coverage diagram. 

For the atmospheric refraction to be strong enough 
to cause trapping of microwaves it is necessary that 
the refractive index of the atmosphere decrease with 
altitude at a sufficiently rapid rate. For convenience 
in dealing with problems of nonstandard propagation, 
a quantity known as the modified refractive index has 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


121 


been defined and is usually denoted by the letter M. 
It depends on pressure, temperature, humidity, and 
height and can be readily calculated from the proper 
nomograms* or from tables,^ or directly from the 
formula.® 

When values of M are computed for various eleva- 
tions from measurements of the pressure, temperature, 
and humidity at those elevations, a graph can be made 
of the value of J\I plotted against height. This M curve 
gives directly a graphical representation of the struc- 
ture of the atmosphere with reference to the existence 
of ducts. A decrease of M with elevation is called an 
M inversion, since under standard conditions M in- 
creases with altitude, and indicates the existence of a 
duct. This, then, is the criterion for the meteorological 
conditions necessary for the trapping of radio waves. 
The top of the duct is taken to be that level at which 
M reaches a minimum (as in Figure 15) and the base 
of the duct the level at which a vertical projection from 
the value of M at the top of the duct intersects the 
lower portion of the Al curve (as in Figure 16) or the 
ground (as in Figure 17). The term ‘Tluct width” is 
used to refer to the thickness of the duct, i.e., the ver- 
tical distance between the top and the base. 

The vertical distribution (a) of temperature and 
(b) of humidity may each contribute to the formation 
of an Al inversion, in the following ways. 

1. A strong temperature inversion tends to lead 
to duct formation. 

2. A rapid decrease of humidity with altitude tends 
to lead to duct formation. 

If the first of these is predominant the duct is said 
to be dry, and if the latter is predominant the duct is 
said to be wet. Often both factors are operative to- 
gether; that is, in the A1 inversion there is both an 
increase in temperature with altitude and a decrease 
in humidity with altitude, the duct being more sen- 
sitive to the effect of the humidity distribution than to 
that of the temperature distribution. 

Types of Al Curves. For purposes of clarification, 
the various types of Al curves that may exist can be 
classified as follows: 

1. Standard type (Figure 12) . In a standard atmos- 
phere Al increases linearly with altitude at a rate of 
3.6 Al units per 100 ft (0.118 Al unit per m). Radio 
and radar waves are bent slightly downward, the paths 
of the rays actually having a radius of curvature about 
four times that of the earth ; but no trapping occurs. 
Standard conditions, in their effect on propagation, 
hardly differ at all from those of neutral and unstable 



equilibrium (except in special cases as mentioned 
later) and so are frequently found in well-mixed air, 
as is likely to occur on sunny afternoons and in areas 
of turbulence. 

2. Transitional type (Figure 13). In the lower 
levels Al is constant with elevation. Correspondingly, 
rays are bent downward more than in the standard case 
but not so strongly as in a duct, i.e., the rays are not 
actually trapped. Being literally a transitional case. 



Figure 13. Transitional type of Al curve. 

this type of Al curve is likely to occur during the 
formation or dissolution of a duct, or when the mete- 
orological factors tending to cause a duct are incom- 
pletely operative. The Al deficit (Ail/, defined in Sec- 
tion 8.3.3), is indicated in the figure. 

3. Substandard type (Figure 14) . In the lower levels 
Al increases more than 3.6 Al units per 100 ft, which 
corresponds to rays being bent downward only very 
slightly or, in some cases, actually upward from the 
line of sight, thus giving shorter maximum ranges on 
surface and low-flying targets. There is no trapping. 
Depending to some extent upon the elevation of the 
transmitter, the field strength in the substandard 


122 


METEOROLOGY— FORECASTING 


region may be reduced considerably below normal, even 
to the point of producing radar and communication 
“blackout.” The M deficit is negative with this type 
of curve. Associated meteorological conditions are 
usually those in which warm, moist air passes over a 



Figure 14. Substandard type of M curve. 

relatively cool land or sea surface, quite frequently in 
connection with the formation of surface fog. 

4. Simple surface trapping (Figure 15). The M 
curve has a negative slope in the inversion layer which 
comes down to the land or water surface. The duct is 
of the ground-based type, and its width is the height 
of the upper boundary of the inversion layer. Eays 
which are propagated at an angle of 1 degree or less 
with the horizontal may be trapped within the duct. 
As a consequence, radio and radar ranges may be 
exceedingly large. Simple surface trapping occurs 
quite frequently over the oceans — particularly where 
warm, dry air from over land flows out over a cooler 
sea surface — along coast lines with an afternoon sea 
breeze, and occasionally over land with radiational 
cooling at night. 




5. Elevated S-shaped type (Figure 16). The inver- 
sion layer has a width given by the difference in eleva- 
tion of the end points of the negative portion of the 
M curve, but the width of the duct extends downward 
to the level where the vertical projection of the upper 
minimum of the M curve intersects the latter. Trap- 
ping occurs when the transmitter is at an elevation 
which places it within (or close to) the duct and is 
most pronounced when the transmitter is at the eleva- 
tion of the base of the M inversion. This type of duct 
may be brought about by subsidence or as the result 
of a Fohn wind blowing off shore from mountains 
paralleling a coast. Examples of elevated S-shaped M 
curves are observed off the southern California coast 
and off the east coasts of Japan and New Guinea (see 
Section 8.3.5). 



Figure 17. Ground-based S-shaped type. 

6. Ground-hased S-shaped type (Figure 17). When 
the conditions which could produce type 5 (Figure 16) 
exist down to the surface of the earth or to the sea, 
this type of duct may occur. It usually has a width 
considerably greater than that found in the simple 
trapping case (type 4, Figure 15). 

That it is possible for ducts of two types to occur 
simultaneously has been shown from observations off 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


123 


the east coast of New Guinea when a Fohn wind flows 
out over a sea breeze, the latter producing simple sur- 
face trapping (Figure 18). (See Section 8.3.5.) 

Factors Affecting the Extent of Trapping. The prin- 
cipal factors which determine the extent of trapping 
are : 



Figure 18. Combination of types 4 and 5. (See Figures 
15 and 16.) 


1. The amount by which M decreases through the 
M inversion. 

2. The duct width, for the wider the duct the 
more energy will be trapped. 

3. The elevation of the transmitter with respect to 
the duct, the trapping being most complete when the 
transmitter is at the base of the M inversion. 

4. The angle at which the rays are propagated from 
the transmitter ; the smaller the angle made with the 
top of the duct, the greater the range. 

5. The frequency of the propagated waves; in 
general, the higher the frequency, tlie greater the 
extent of trapping. 

Specific Relationships Between 
Meteorological Elements and 
Radar Performance 

Research on Forecasting of Radio 
AND Radar Ranges 

Arniij Air Force Board Project. Realizing the im- 
portant and direct effects of temperature and humidity 
distributions on microwave propagation, several proj- 
ects have been undertaken in the attempt to develop 
a systematic method of forecasting the meteorological 
conditions leading to nonstandard propagation. Of 
these methods, one which has met with a considerable 
degree of success is described below. The methodology, 
developed by the Army Air Force Board working in 
conjunction with the Radiation Laboratory at MTT,® 
is designed to predict the formation of surface ducts 


over water. Its fundamental concepts are quite similar 
to those used in other methods of radio and radar 
forecasting.^® 

General Procedure. In essence the method consists 
of an analysis of the modification that air undergoes 
in the lower 1,000 ft as it moves from a large land mass 
out over the ocean. The study was carried out in the 
vicinity of Cape Cod, but indications are that the 
numerical factors entering into the procedure are 
much more generally applicable. In the modification 
of the air moving over the sea, the following assump- 
tions are made. 

1. The air initially (before moving off the land 
mass) is well mixed, i.e., it exhibits conditions close 
to neutral equilibrium (see Figure 11). 

2. The stability conditions of the air as it moves out 
over water are determined by its initial temperature 
(over land) relative to that of the sea surface. 

3. The modified air at the sea surface acquires the 
same temperature as the sea. 

4. In the modified air at the sea surface the mois- 
ture content becomes that corresponding to satura- 
tion at the sea surface temperature, except for a cor- 
rection owing to the salinity of the sea. 

5. The resulting ilf curve is determined by the 
quantities : 

a. Temperature excess.^ 

b. M deficit.^ 

e. Wind speed and direction. 

d. Distance of over-sea travel (in some cases). 

Thus the method attempts to relate duct formation 
to a limited number of easily determined meteoro- 
logical factors. It involves a simplified consideration 
of the upward diffusion of heat and moisture. It turns 
out, however, that the simplified assumptions yield 
results which in practical application are of sufficient 
accuracy to be of definite use in forecasting the ex- 
istence of nonstandard conditions. It should also be 
mentioned that, although the method is designed 
primarily for situations in which air over land moves 
out over the sea, it can also be satisfactorily applied 
to situations in which the air has a purely over-sea 
trajectory. 

The particular steps to be taken in carrying out the 
procedure follow. 

Method of Determining Duct Width 

Observation of Initial Conditions. The necessary 
meteorological measurements to be taken should be 

^These terms are defined on page 124. 


124 


METEOROLOGY— FORECASTING 


as representative as possible, i.e., uninfluenced by 
purely local effects. Measurements are : 

1. Surface air temperature (of the unmodified air 
over land, in the case of air moving off a land mass) ; 

2. Surface air humidity (also of the unmodified 
air which can be expressed in terms of relative humid- 
ity, specific humidity, dew point, wet bulb tempera- 
ture, or vapor pressure) ; 

3. Sea surf ace temperature ; 

4. Wind speed and direction (preferably at 1,000 ft- 
elevation) ; and sometimes 

5. Distance from land (of primary importance only 
in the case of stability conditions, when the air is 
warmer than the sea surface). 

All these data may, of course, be profitably supple- 
mented by aerological soundings, weather maps, and 
any other pertinent information available. 

Modification of Air hy Sea Surface. As a qualitative 
description of the modification that the air undergoes 
in moving over water, three cases may be distinguished, 
namely : 

1. Neutral equilibrium (resulting when the initial 
surface air temperature is the same as the sea temper- 
ature). The temperature structure of the air remains 
unchanged ; however, since the air is usually not com- 
pletely saturated, moisture is supplied to the lower 
layers by evaporation from the sea surface, in this way 
causing a greater decrease of humidity with height, 
which tends to establish an M distribution such that 
the modified refractive index is either constant or 
decreasing with height. In the case in which the air 
is initially completely saturated no modification takes 
place. 

2. Unstable equilibrium (resulting when the initial 
surface air temperature is less than the sea surface 
temperature). In this case the moisture content of the 
air is always less than that corresponding to satura- 
tion at the sea surface temperature, so that the lower 
layers of air suffer an increase in humidity as well as 
in temperature. Owing to the greater sensitivity of 
M to humidity than to temperature this tends to bring 
about a decrease of M with height in a layer of air 
adjacent to the sea surface, while the unstable condi- 
tions give rise to vertical mixing which keeps the M 
distribution close to standard above this layer so that 
the duct is confined to lower levels than in the case of 
neutral equilibrium. 

3. Stable equilibrium (resulting when the initial 
surface air temperature is greater than the sea sur- 
face temperature). If, in addition, the air is initially 


quite dry, i.e., has a moisture content less than that 
corresponding to saturation at the sea surface tempera- 
ture, then the resulting rapid decrease of moisture with 
height plus the stable temperature distribution leads 
to a tendency to surface duct formation. On the other 
hand, if the initial moisture content of the air is rela- 
tively large, moisture may be condensed out of the 
surface layers of air thus tending to give rise to an 
increase in humidity with elevation which when suffi- 
ciently marked may counteract the effect of the stable 
temperature distribution and so prevent the forma- 
tion of a duct or even produce substandard conditions. 
In either case, the stable structure of the air tends to 
hinder vertical mixing so that modification from the 
surface upward proceeds slowly and hence is highly 
dependent on the distance traveled by the air over 
the water. 

Necessary Calculatio7is. To determine quantitatively 
the possibilities of duct formation, the following items 
can be readily calculated from any particular observed 
set of initial conditions. 

1. Temperatwe excess, which is merely the repre- 
sentative surface air temperature (before modifica- 
tion) minus the sea surface temperature. 

2. M deficit, defined as the value of M correspond- 
ing to the sea surface temperature minus the value 
of M determined from the representative surface air 
temperature and humidity (before modification); 
values of M can be ascertained from nomograms,'* 
tables,' or directly from the formula.^ In the case of 
M corresponding to the sea temperature, a 98 per cent 
saturation is assumed; the 2 per cent vapor pressure 
correction is subtracted to take into account the salin- 
ity of the sea water. 

3. Ratio of duct width to M deficit, determined 
from the chart in Figure 19 for a given temperature 
excess and wind speed as measured at the 1,000-ft 
level. 

4. Duct width, found by multiplying the above 
ratio (3) by the M deficit. 

Applicability of the Method. Since the procedure 
is designed to take into account only the surface modi- 
fication of air over water, its application is restricted 
to the prediction of the first four types of M curves 
described in Section 8.3.2: standard, substandard, 
simple surface trapping, and transitional. The causes 

'‘Nomograms are included and explained in the Appendix. 

'Tables for computing M can be found in references 8 and 9. 

'The formula expressing M in terms of pressure, temper- 
ature, humidity, and elevation is given in the Appendix. 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


125 


of S-shaped M curves are not considered in this 
method. Standard conditions can be presumed to 
occur when the calculations indicate a duct width of 
zero, which is the case when the M deficit is zero. If 
the M deficit is negative, then the calculated duct 
width will be negative, and substandard conditions are 
• to be inferred. A positive M deficit indicates duct 
formation (simple surface trapping), and the calcula- 
tions of the duct width given an estimate of the height 
to which the duct extends. If this height is small, 
conditions may be inferred to correspond to the tran- 
sitional case. Once the duct width is calculated, a 
complete picture of the distribution of M with height 
can be approximated as indicated in Figure 15 by 
assuming that standard conditions prevail above the 
duct and that the M deficit (AM) is the difference 
between the actual M value at the sea surface and 
the M value that would exist at the sea surface if the 
standard conditions were extended down to the surface. 

The method is not applicable to conditions over 
land. 

In the case of air with a purely sea trajectory, it 
turns out that the procedure is closely valid if, in 
place of the air temperature and humidity measure- 
ments made over land, these measurements are taken 
in the air at a slight elevation above the sea surface, 
for example, at bridge level on a large ship. 

In practical application results will be most reliable 
when the assumptions listed under ^^General Proce- 
dure” are satisfied. However, this does not mean 
that the method is useless under other circumstances. 
Figure 19, which is the crux of the method, is largely 
empirical and is based on relationships which have 
been observed to hold under various meteorological 
conditions. Consequently, reasonably accurate results 
are not limited to only a few idealized situations. 

It should be mentioned also that use of the method 
in a literal manner can be improved upon if the cal- 
culated results are modified by the judgment of 
someone trained or experienced in meteorology. Com- 
plicating factors such as variations in the initial sta- 
bility conditions, variability of the sea surface tem- 
perature, effects of convergence, divergence, and sub- 
sidence, and presence of fronts can best be taken into 
account by one familiar with their effects. 

Qualitative Pkediction of Eadar Eanges 

The method described above gives a means of esti- 
mating surface duct formation, whereas what is needed 
is a knowledge of the effect of the duct on radio propa- 
gation. It is impossible to make a blanket statement 


LIMITED TO OVER-WATER NO TRAVEL 
TRAVEL 10-30 MILES LIMITATION 



I I I I I \ I I 

5 0-5 

TEMPERATURE EXCESS IN DEGREES C 

Figure 19. Graphs showing the value of the ratio of 
duct width d to the M deficit, AM for values of temper- 
ature excess and wind speed at the 1,000-ft level. 
(Typical values are given in Table 2.) 

giving the exact range that will be obtained with any 
particular duct width, since the range depends on the 
power of the radio or radar set (also on the character 
of the target, in the case of radar), as well as on the 
factors listed in Section 8.3.2. However, some numer- 
ical estimates of trapping effects can be made. 

Dependence on Duct Width, Frequency, and Eleva- 
tion of Site. An approximate expression relating the 
maximum wavelength that can be trapped by surface 
ducts is given by 

An,ax = 0.0766ZVAilf-^0.0366Z, 

in which Amax is the maximum wavelength in centi- 
meters, d is the duct width in feet, and Ailf is the M 
deficit in M units. Table 2 is developed from this 
formula and indicates, for given values of Ailf and d. 


126 


METEOROLOGY— FORECASTING 


the wavelength above which trapping will not occur. 
A rough generalization can be made by stating that, 
when the wavelength of the radiation is around 3 cm, 
duct widths of 20 ft or more will be sufficient to cause 
simple surface trapping, and, when the wavelength is 
around 10 cm, duct widths of at least 40 or 50 ft will 
be sufficient, provided in each case that the transmitter 
is located within the duct. Thus, for a particular radai- 
frequency and location, an estimation of duct width 
becomes a critical factor in anticipating whether an 
appreciable amount of trapping will occur and con- 
sequently whether radar ranges will be appreciably 
larger than under standard conditions. 


Table 2. Values of the maximum wavelength (in cm) 
for which waves can be trapped in a surface duct for 
given values of M deficit (AM) and duct width {d). 


d(ft) 

2 

5 

AM 

10 

(M units) 
15 

20 

25 

10 

0.97 

1.63 

2.36 

2.90 1 

3.36 

3.78 

20 

1.72 

3.14 

4.62 

5.75 

6.67 

7.49 

30 

2.19 

4.52 

6.80 

8.50 

9.93 

|ii.i 

40 

2.28 

5.74 

8.88 

1 11.2 

13.1 

14.7 

50 

1.69 

6.80 

10.9 

13.8 

16.2 

18.3 

60 


7.65 

12.8 

16.3 

19.2 

21.8 

70 


8.35 

14.5 

18.8 

22.2 

25.2 

80 


8.82 

16.2 

21.2 

25.2 

28.6 


Dependence on Extraneous Factors. Meteorological 
conditions other than ducts often have important 
effects on propagation. Surface fog frequently causes 
substandard conditions. Rain and clouds may attenu- 
ate the propagated energy and effectively decrease 
the range. Heavy rain and sometimes cumulo nimbus 
clouds cause radar echoes. 

Opekational Use and Limitations 

The restrictions surrounding the possible utilization 
of this prediction technique have been covered earlier 
in this section, where it is indicated in what respects 
applicability is ’limited. Subject to these limitations, 
the method can be employed to advantage. Short-term 
predictions (a day or so ahead) of duct formation and 
radar range can aid in estimating the coverage of a 
particular radar set. Information of this nature should 
lead to the more efficient use of radar facilities. 

Computed Climatological Information 
on Surface Ducts 

Purpose of This Information 

Inasmuch as the present report is designed to aid 
radar and meteorological officers in the Pacific theater 


of war, it has been thought expedient to include 
climatological information on that area which gives 
an indication of the occurrence of surface ducts. For 
this purpose, computations have been carried out, 
using the methodology presented in Section 8.3.3, to 
yield the following : 

1. Estimation of the per cent of time surface ducts 
of certain widths are likely to occur at various times 
of the year and at various places in the western Pacific 
theater. 

2. Estimation of the variation in duct width with 
the time of year, geographical location, etc. 

3. Estimation, from (1) and (2) above, of the 
amount of trapping to be expected for specified radio 
frequencies and specified elevations of sites. 

Regions Chosen for Study 

The area chosen for investigation was that bounded 
approximately by 10° and 50° N latitude and by 120° 
and 150° E longitude. These regions include the Japa- 
nese islands, the coasts of Korea, Manchuria, and 
China, northern Philippines, the Marianas, the 
Bonins, and the Ryukyu Islands. The computations 
were carried out for representatively selected 5x5 degree 
sectors or “squares.’^ The results for several regions 
in this area are summarized and are given below. 

Sources of Climatological Data 

The charts and atlases used in compiling the data 
can be found in references 11 to 15. 

Method of Computation 

The procedures described in Section 8.3.3 were ap- 
plied as follows: 

1. A determination of the monthly mean tempera- 
ture excess was made for each 5x5 degree square for 
each month (1) by taking the difference between the 
mean temperature of the air over the sea and the mean 
sea surface temperature, and (2) by taking the differ- 
ence between the mean temperature of the air at a land 
station (when the given square was near a coast) and 
the mean sea surface temperature. 

2. A determination of the monthly mean M deficit*^ 
was made for each square for each month using the 

‘‘These calculations do not represent exactly the correct 
mean value of the M deficit, since M is not a linear function 
of the temperature and humidity, and so the value of M com- 
puted from mean temperature and humidity data is not quite 
the same as the mean of all M’s computed from individual 
temperatures and humidities. A cursory evaluation of this 
error has indicated that the values computed are if anything 
conservative, i.e., that the actual mean M deficits are prob- 
ably larger than those computed. 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


127 


nomograms and taking the data for (1) the mean 
temperature and wet bulb depression of the air over 
the sea and the mean sea temperature, and (2) the 
mean temperature and relative humidity of the air 
at a land station (when the given square was near a 
coast) and the mean sea temperature. 

3. For each square for each month note was made 
of the various surface wind velocity ranges that oc- 
curred with each wind direction (eight points of the 
compass) and the percentage of time the wind lay 
within each velocity range.^ 

4. In terms of the mean temperature excess and 
mean M deficit, the corresponding duct width was 
computed for each wind velocity range, and, knowing 
the percentage of time that winds of each magnitude 
occurred, it was possible to compute the percentage of 
time that ducts of various widths would occur, both 
for each wind direction (on an eight point compass) 
and for the overall picture regardless of wind direction. 

Results of Computations 

The results were summarized by lumping individual 
squares showing similar characteristics into nine re- 
gions within the whole area. In each region data for 
the individual months were lumped together on the 
basis of similarity to divide the year into three or four 
parts (these varying according to region). Then for 
each group of months in each region were listed those 
results which were considered to be the most impor- 
tant, namely, 

1. The range in duct widths, giving an indication 
of the variability at any one place at any one time 
of year. 

2. The percentage of time that ducts characterized 
by widths greater than 40 ft occur and, following this, 
the most prevalent wind direction associated with 
ducts of these widths, as well as the minimum wind 
velocity necessary to establish them. 

3. The percentage of time that ducts characterized 
by widths from 20 to 40 ft occur, similarly followed 
by the associated prevailing wind direction and the 
minimum required wind velocity. 

4. The percentage of time that ducts do not occur 
or have a width less than 20 ft. 

Figure 20 contains these summarized results. The 
numerical listings in the figure make no claim toward 

‘This led to a slight error, inasmuch as the wind at 1,000 ft 
should have been used in place of the surface wind (data 
were available only for the latter). This error in most cases 
resulted in calculated duct widths of slightly less magnitude 
than would have been obtained if the l,()00-ft wind had 
been used. 


being exact, as is evident in view of the remarks made 
in Section 8.3.3 on the applicability and limitations 
of the method, in addition to the slightly erroneous 
computations of the monthly mean M deficit and the 
use of the surface winds instead of those at 1,000 ft. 
(The effect of the latter two errors is mainly to cause 
the calculated duct widths to tend toward the conserva- 
tive side.) In Figure 20, for purposes of consistency 
throughout the area, only the calculations based on 
air temperature and humidity records over the sea 
were used [i.e., only (1) under ^‘Method of Compu- 
tatioiF^]. The difference between these calculations 
and those based on land station data is primarily that 
temperature excesses and M deficits are larger in the 
latter case (this again tends to make the tabulated 
results conservative). 

Other deficiencies of the method which might be 
cited are the neglect to take into account the occur- 
rence of fog or rain (which tends to create substandard 
or standard conditions) and the omission of the in- 
fluence of local effects such as the topography along 
coast lines (see Section 8.3.5). In some cases the 
period of record was fairly short, so that the data 
used in the calculations were not always completely 
representative. Lastly, the ranges of duct widths were 
calculated on the assumption that there was a varia- 
tion of wind speed only, not allowing for possible 
variation in temperature excess and M deficit. 

In spite of these shortcomings, the calculated re- 
sults show regional and seasonal trends consistent 
both with what might be expected on the basis of 
qualitative physical reasoning and also with a limited 
number of actual observations taken in the Pacific 
(see Section 8.3.5). In conclusion we may safely state 
that the results represent to a reasonable approxima- 
tion the average conditions of surface duct width and 
variability. 

Use of Computed Results 

Since the computations are based on climatological 
data and are limited in exactness, they do not have 
forecasting value in the sense of indicating specifically 
what trapping conditions will be on any particular 
day. They serve merely to indicate in a general way the 
average conditions that might be expected over a pe- 
riod of time. For example, the percentage of time that 
duct widths in excess of 40 ft occur gives an estimate 
of the fraction of time that properly sited S- or X- 
band radars would be able to take advantage of ex- 
tremely large ranges ; the percentage of time that duct 
widths from 20 to 40 ft occur indicates that portion 


128 


METEOROLOGY— FORECASTING 



JFMAMJ 

JASOND 


0-15 

0 

0 

100 


N D 

J F 

M A 

M J 

J A 

S 0 

5-40 

5-30 

0-25 

10-40 

5;NW,>50 

0 

0 

5iNE,>50 

50»NW,>20 

50iN,>25 

lOi— ,>40 

55iNE,>IO 

45 

50 

90 

40 


J F M 

A M J 

J A 

S 0 

N 0 

5-40 

15-30 

20-45 

10-50 

5iNW,>50 

0 

lO-,— ,>40 

I5;NW,>30 

60iNW,>20 

m 

A 

r 

6 

65-,— , >5 

55»— ,>I0 

25 

30 

25 

30 


D J 

F M 

A M J 

J A 

S 

0 N 

5-40 
5;NW,>50 
45i NW,>20 
50 

15-30 

0 

70i— , >10 
30 

25-40 
5»— ,>40 
85;—,— 

10 

10-50 

IOiNW,>30 

50;N,>I0 

40 


J F M 

A M J J 

A S 0 

N D 

15-50 
20; — ,>25 
60-,—, >10 
20 

25-40 
5;—, - 
95;-,— 

0 

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10;-,— 

80;-,- 

10 


0 J 

F M 

A M J 

J A 

SON 

25-45 
I0;E.>30 
90. E; — 

0 

30-45 
5;—, — 
95;E, — 

0 

30-50 
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0 

1 1 1 o 


130 

LEGEND 

HEAVY LINES SEPARATE THE OCEANIC REGIONS. 

MONTHS (DECEMBER, JANUARY AND FEBRUARY). 3- 
RANGE OF DUCT WIDTH IN FEET (5 TO 30 FEET). 3 
PERCENTAGE OF TIME DUCTS OF WIDTH GREATER THAN 40 
FEET OCCUR (0 PER CENT). 

PERCENTAGE OF TIME DUCTS OF WIDTH 20 TO 40 FEET OCCUR 1 
(30 PER CENT); PREVAILING WIND DIRECTION WITH DUCTS OF 
THESE WIDTHS (NORTH), WIND VELOCITY NECESSARY TO CAUSE 
DUCTS OF THESE WIDTHS (GREATER THAN 20 MPH). 

PERCENTAGE OF TIME DUCTS OF WIDTH LESS THAN 20 FEET“l 
OCCUR ( 70 PER CENT). 


0 J F 

M A 

M J J 

A S 

0 N 

10-50 
20;NE,>25 
60, NE, >5 
20 

20-40 
10;-, >35 
80iNE,>5 

10 

25-40 
5;-, - 
90;-,— 

5 

20-40 

10;-,— 

80;NE,— 

10 


0 J F 

MAM 

J J A 

S 0 

N 

5-30 

0 

50;N,>20 

70 

15-25 

0 

50; SE,— 
50 

20-35 

0 

90;NE,>5 

10 

10-40 

5;N,>50 

55;N,>IO 

40 


V J F 

MAM 

J J A 

S 0 

N 0 

5-30 

0-20 

10-35 

5-40 

0 

0 

0 

5;—, >50 

I5;NE, >25 

5;— — 

50;N,>I0 

30;— ,>20 

85 

9i 

50 

65 


Figure 20. Summarized results of climatological duct with calculations. 


of the time in whicli X-band radars would be needed 
to benefit from surface duct conditions; the percentage 
of time that no ducts (or exceedingly small ducts) 
occur points out limitations in the utilization of 
simple surface trapping. Inasmuch as the transmitter 
should be located within the duct (if the maximum 
benefit is to be received from trapping conditions), 
these factoi’s indicate preferalile elevations of the 


transmitter. In general, the information given in Fig- 
ure 20 can be helpful in relatively long-range plan- 
ning procedures, in deciding on tlie most effective 
type of radar set, the optimum frequency to use, and 
the most advantageous elevations at which to estab- 
lish sites, etc., for operations to be conducted during 
a particular season of the year and in a particular 
region. 


APPLICATION OF FORECASTING TECHNIQUES AND CLIMATOLOGY 


129 


8.3.5 Direct Indications of Nonstandard 
Conditions in the Western Pacific 

Geneeal Conclusions 

Evidences of superrefraction have frequently been 
found at Guadalcanal and in the general vicinity of 
New Guinea and New Zealand. Data obtained on the 
radio-meteorology of the western Pacific in the region 
from New Guinea to Saipan, from soundings made 
there in 1944 and 1945/®'^® indicate the following con- 
ditions in both the equatorial and trade wind belts of 
the Pacific. 

1. Unmodified winds of long sea trajectory pro- 
duce ducts which attain sufficient height and intensity 
to trap microwaves in the 3,000- to 10,000-mc range. 

2. At the relatively low wind speeds characteristic 
of the equatorial belt (4 to 10 knots), the duct height 
increases with wind speed from about 20 to about 40 
ft. X-, and possibly S-, band radars with properly 
placed antennas may be expected to show marked in- 
crease in range on surface craft and on aircraft flying 
within the duct. 

3. At the higher wind speeds typical of the trade 
wind belt (10 to 20 knots), ducts 50 to 60 ft wide 
occur regularly. Properly sited S-, as well as X-, band 
radars may be expected to show marked and persistent 
increases of range on surface targets. The persistence 
of the duct in these regions suggests its use in micro- 
wave communications. 

4. Unless modified by passage over nearby land 
masses, the atmosphere is approximately standard 
from 60 to 1,000 ft. 

5. The results are so similar to earlier measure- 
ments taken in the Caribbean on northeast trade wind 
air of long sea trajectory as to warrant the conclusion 
tliat this type of duct formation is general, at least in 
tropical and subtropical regions, throughout the world. 

6. From the experimental results around Saipan 
and the Marianas it is concluded that the coverage of 
radars operated at frequencies much lower than 3,000 
me will probably not be affected by the oceanic ducts. 

7. The coverage of microwave radars (3,000 me 
and higher) which are sited above 100 ft may not be 
affected by low-level conditions. 

8. If coverage on surface craft or ultra-low-flying 
aircraft beyond the range of existing facilities is re- 
quired and if prevailing wind speeds exceed 10 knots, 
S-band radars sited 10 to 30 ft above sea level may 
give better results than high-sited ones. 

9. X-band radars sited at 10 to 20 ft should be 
useful down to wind speeds of the order of 6 knots. 


10. In microwave communication links, the use of 
low-sited antennas may increase range beyond that 
attainable by siting at the highest available altitudes. 
(From the standpoint of water vapor attenuation and 
duct utilization, X-band frequency appears to be the 
optimum for this purpose.) 

11. From a series of ship-based kite soundings tak- 
en northeast of Saipan in the two distinct weather 
regimes, ( 1 ) a typical fair weather period, with steady 
10- to 20-knot trades blowing and (2) a stormy period 
with variable 4- to 15-knot southerly winds and fre- 
quent rain squalls, it has been found that all sound- 
ings yield simple surface trapping curves exclusively, 
the average duct widths being respectively (1) 44 ft 
and (2) 37 ft. 

12. Although measurements were not taken under 
the conditions mentioned in paragraph 11 (2) above, 
soundings immediately after the squalls showed the 
usual duct. (Sea surface temperatures were constant 
at 84 to 85 F. Close to the surface the temperature 
lapse rate was superadiabatic, but it was dry adia- 
batic above 100 ft.) 

Observations upon Ducts other than 
Simple Surface Trapping 

Although the emphasis in this report is placed upon 
simple surface trapping, nonstandard propagation is 
found under other distributions of atmospheric mois- 
ture and temperature. Elevated inversions are found 
up to around 5,000 ft, due to subsidence in anti- 
cyclones over the Pacific"; the western and the 
southern portions of this' area usually exhibit the 
higher elevations. Illustrative of one of the other fac- 
tors in nonstandard propagation is the Fohn wind 
which often produces an elevated S-shaped duct and 
frequently is superimposed upon a sea breeze. Figure 
21, plotted from data taken in the vicinity of the 
800 
700 

^ 600 

UJ 

u! 500 

z 

K 400 

X 

o 

w 300 

X 

200 

100 
0 

74 78 82 86 13 17 21 25 29 370 375 380 385 390 395 

TEMPERATURE MIXING RATIO M 

IN DEGREES F G/KG 

Figure 21. Data from Geelvink Bay, New Guinea, 
showing surface duct as well as elevated S-shaped duct 
due to Fohn effect from 10,000-ft mountains 100 to 150 
miles to windward (SW). 



130 


METEOROLOGY— FORECASTING 


New Guinea coast/® indicates the occurrence of an 
elevated S-sliapcd curve, below wliich is found simple 
surface trapping or the usual trade wind surface in- 
version. While the existence of conditions favorable 
to such effects off the coasts of J apan may be assumed, 
on account of the lofty mountains, there are no 
data available on this point. The only information on 



-8 -6 -4 -2 0 

M-Mq 

Figure 22. M deficits calculated from soundings made 
at Tateno, Honshu, 1928. 

trapping in the Japanese area has been obtained from 
a study of soundings made in 1928 at Tateno,^® on the 
east coast of Honshu, some fifty miles from Tokyo. 
The data, plotted in Figure 22, shows three cases of 
an M inversion. The numerical quantities are given 
in Table 3. 


Table 3. Aerological soundings at Tateno, Honshu, in 
1928, together with computed duct widths and the magnitude 
of the M deficit. 


Date 

Elevation 
of duct 
top (ft) 

Elevation 
of duct 
base (ft) 

Duct 

width 

(ft) 

Magnitude 
of M 
deficit 

May 1 

1,900 

1,300 

600 

-6 

August 23 

1,000 

650 

350 

-5 

September 29 

1,250 

950 

300 

-2 


Note on Attu and the x^leutians^®’^^ 

Fixed echoes have been obtained at abnormally 
long ranges (100 to 150 miles). The ‘^‘Battle of the 
Pips” was an illustration of pronounced superrefrac- 
tion. The latter has been observed on at least four 


occasions by operators of airborne radars returning 
to Attu from missions over the Kuriles, when YHF 
l adar beacons have returned signals to planes at 5,000 
ft and 300 to 350 miles, or about three times the 
horizon line distance. Meteorological data on duct 
conditions during the cycle of the Aleutian seasons 
are needed (up to 1,000 ft). 

APPENDIX 

Staxuauu Atmosphere 

Definition. The National Advisory Committee on 
Aeronautics [NACA] defines the ‘^‘standard atnios- 
pheie” as that which exhibits: 

1. A sea level pressure of 1,013 mb (=160 mm of 
meiT'ury = 29.92 in. of mercury). 

2. A sea level temperature of 15 C (= 59 F) Avhich 
decreases at a rate of 6.5 C per km ( = 3.41 F per 1,000 
ft) in the lower atmosphere; and in addition the 
moisture content may be specified as follows: 

3. A relative humidity of 60 per cent, which corre- 
sponds to a water vapor pressure of approximately 10 
mb at sea level and to a rate of decrease in the lower 
atmosphere of about 1 mb per 1,000 ft. 

Properties. The following table for the standard 
atmosphere indicates the variation with height of (a) 
temperature, (b) pressure, (c) water vapor pressure 
for 60 per cent relative humidity, (d) a quantity con- 
taining the index of refraction, n, and (e) the modi- 
fied refractive index, M. 


Water vapor 
Temper- Pres- pressure for 
Altitude ature sure 60% RH 


Meters Feet 

C 

F 

(mb) 

(mb) 

(n-1) X 106 

M 

0 

0 

15.0 

59.0 

1,013 

10.2 

322 

322 

150 

492.1 

14.0 

57.2 

995 

9.6 

316 

339 

300 

984.3 

13.0 

55.4 

977 

9.0 

309 

357 

500 

1,640.4 

11.7 

53.1 

955 

8.3 

300 

379 

1,000 

3,280.8 

8.5 

47.3 

894 

6.7 

281 

438 

1,500 

4,921.2 

5.2 

41.4 

845 

5.3 

266 

501 


Radio Meteoi{ology Teiims 
Index of Refraction. This can be defined for any 
liarticular medium as the ratio of the velocity of 
electromagnetic waves in a vacuum to their velocity 
in the medium. The relationship indicating the 
amount of bending or change in direction that occurs 
as electromagnetic radiation crosses a boundary be- 
tween two media with different refractive indices is 
given by SnelPs law: 

Ui cos ai — n 2 cos a 2 

in which n^ is the refractive index of the first medium, 


APPENDIX 


131 





Figure 23. Psychrometric nomogram. 



132 


METEOROLOGY— FORECASTING 


/ig that of the second medium, the angle which the 
ray in leaving the first medium makes with the boun- 
dary, and ag the angle which the ray in penetrating 
the second medium makes with the boundary. In the 
case of the atmosphere (one medium with a variable 
refractive index) this expression can be modified to 
relate the gradual bending of a ray to the manner in 
which the refractive index varies. The value of the 
refractive index, n, at any particular point in the 
atmosphere can be determined from measurements of 
pressure, temperature, and humidity by substitution 
in the formula, 



or, expressed differently. 



in which the temperature, T, is measured in °K, and 
the atmospheric pressure, p, and vapor pressure, e, 
in millibars. 

Modified Refractive Index. It is considered more 
convenient, in problems of radio propagation, to de- 
fine a slightly different quantity M, which is related 
to the index of refraction by 



in which n is the index of refraction, a is the radius 
of the earth (21 X lO"’ ft) and h is the height above 
the surface of the earth (measured in the same units 
as a). In terms of pressure, temperature, humidity, 
and height, M is given by 

„ 79 / , 4800e\ , 

M=^[p + ^)+-pO^, 

in which the units of measurement used are the same 
as above. The rate at which M increases with altitude 
is given by 



which in the standard atmosphere is 

— -0.039 + 0.157 

dh 

= 0.118 M unit per meter 
= 0.036 M unit per foot. 

Psychrometric Nomogram. Radiation Laboratory 
(MIT) has developed a nomogram with which to 
compute the modified index of refraction from the 


necessary meteorological parameters. This chart is 
known as the psychrometric nomogram. (See p. 131.) 

Meteorological Terms 

Absolute Humidity. The mass of water vapor pres- 
ent in a unit volume of air is known as the absolute 
humidity of the air. It is another way of expressing 
the water vapor density. 

Specific Humidity. The specific humidity of moist 
air is the ratio of the weight of water vapor mixed 
with the air to the weight of the moist air. If p is the 
barometric pressure and e is the partial pressure of 
tJie water vapor, then the specific humidity is given by 

g 

Q = 622 gperkg . 

p — 0.377c 

Mixing Ratio. The ratio of the mass of water vapor 
mixed with unit mass of perfectly dry air is known 
as the mixing ratio and may be expressed as 

w = 622 g per kg . 

p-e 

Relative Humidity. The ratio of the actual water 
vapor pressure to the saturation vapor pressure at the 
same temperature is known as the relative humidity 
of moist air. If e and Cg are the respective vapor pres- 
sures, then (in per cent) the relative humidity is 
expressed as 

mi = - X 100 . 

e. 

Wet Bulb Temperature. The lowest temperature 
to which a wetted ventilated thermometer can be 
brought by evaporation is called the wet bulb tempera- 
ture. It is not strictly an air temperature. 

Air Mass. An extensive body of air which approxi- 
mates horizontal homogeneity is known as an air 
mass. The four principal types are illustrated by the 
accompanying table. 


Source 

region 

Moisture 

classifi- 

cation 

Thermal 

classifi- 

cation 

Name 

Symbol 

Land 

Dry 

Hot 

Tropical continental 

cT 



Cold 

Polar continental 

cP 

Oceanic 

Wet 

Hot 

Tropical maritime 

mT 



Cold 

Polar maritime 

mP 


Front. The surface of separation between dissimilar 
air masses is known as a frontal surface. On a surface 
weather map a ‘^TronR^ is the intersection of this sur- 
face with the surface of the earth. 

Dry Adiabatic Lapse Rate. When dry air ascends 
so as to expand adiabatically, it is said to cool at the 


APPENDIX 


133 


dry adiabatic lapse rate (5.5 ¥ per 1,000 ft or 1 C 
per 100 m). There must be no condensation or evapora- 
tion of associated water vapor during the process. 

Subsidence . An extensive sinking process, result- 
ing in d 3 uiamically heated air and an increase in 
stability, most frequently observed in anticyclones, is 
known as subsidence. 

Instructions for Use of Nomogram 

This nomogram (Figure 23) may be used to com- 
pute M when temperature is expressed in degrees 
Fahrenheit or centigrade, humidity in terms of wet 


bulb (degrees Fahrenheit or degrees centigrade), dew 
point (degrees centigrade), or vapor pressure (milli- 
bars), and height in feet or meters. Place a straight- 
edge so as to align the temperature on scale 1 with the 
wet bulb temperature on scale 3 (or with the dew point 
or vapor pressure on scale 4). The point at which the 
straightedge intersects scale 6 indicates the value 
of the modified index uncorrected for height. Pivot 
the straightedge at this point (on scale 6) so that 
it crosses scale 2 at the desired height. Then read the 
value of M where the straightedge crosses scale 5. 




PART HI 


MI SC ELLA NEO US EXPER IMENTS 




Chapter 9 

REFLECTION COEFFICIENTS 


9 1 REFLECTION COEFFICIENT MEASURE- 
MENTS AT THE RADIATION 
LABORATORY^ 

D ueing the lattek part of 1943 the S-band reflec- 
tion coefficient measurements begun in the spring 
and reported at the July 1943 conference have been 
carried on, and work of a similar nature has been 
started to determine X-band values. The interference 
pattern was observed by recording field strength as a 
function of distance with both receiver and trans- 
mitter heights held constant. One end of the path was 
ground-based, while the other end was carried in an 
airplane which flew over sea toward the land station 
at a constant altitude and bearing. A one-way c-w path 
was used, the transmitters, receivers, and recorders 
being identical to those used previously. The time con- 
stant of the receiver and recorder was 0.3 sec, corre- 
sponding to 0.01 mile for the usual air speeds used. 

When appreciable specular reflection was obtained, 
a regular succession of maxima and minima were 
observed on the record. The product of the divergence 
factor and reflection coefficient was found by deter- 
mining the ratio of electric field strength at adjacent 
maxima and minima. The geometrical expression for 
the divergence factor was assumed correct and all 
variations were lumped in the experimental value of 
the reflection coefficient. It was required that a record 
give a check on the positions of maxima and minima 
for standard refraction and that the maxima obey 
the 1/R'^ law (power) before the record would be 
worked up. 

Flights over land made in 1943 at Orlando, Florida, 
Eiverhead, Long Island, and Cambridge, Massa- 
chusetts, fail to show a regular interference pattern. 
There is a more or less erratic variation of field in- 
tensity with distance, but the magnitude of the varia- 
tion is generally small, and the records obey the 
1/jR^ law. It is believed that the terrain is rough 
enough to scatter all incident radiation of micro- 
waves and that specular reflection will therefore not 
be observed. There is considerable evidence, however, 
that if a microwave transmitter is placed at a fairly 

*By W. J. Fishback, Radiation Laboratory, MIT. 


low height over terrain as smooth as an airport run- 
way, specular reflection will be observed. 

Observations over sea made late in 1943 on S band 
with horizontal polarization have not agreed with 
earlier results. A correlation has been found between 
wind (and presumably wave) direction with respect 
to the path and the magnitude of the reflection coeffi- 
cient. The correlation suggests that low values ob- 
served are due to back scattering. Figure 1 shows lines 
drawn as a means of the values observed on the 4 days 
when exceptionally good flights were made during the 
winter. On November 25, the wind was blowing across 


o 



Figure 1. Reflection coefficient, horizontal polarization, 
versus ’grazing angle. Sea water. Wavelength — S-band. 


the path, and high values of the reflection coefficient 
were observed. On November 22, the wind was blow- 
ing along the path, and low values were observed. 
On December 29 and 30, the wind was blowing 
obliquely with respect to the path and intermediate 
values were observed. While the values on any given 
flight lie fairly close to the lines, there is a consider- 
able amount of scatter. This scatter is now believed 
to be real and supports the results obtained by the 
British. 

Figure 2 shows the results obtained this winter on 
S band with vertical polarization. The values ob- 
served fall about the theoretical curve. If any corre- 
lation with wind direction exists, it is masked by the 
variation within a single flight. 

Equipment difficulties have just been overcome 
and work is getting under way to determine X-band 
values. One flight made on horizontal polarization 


137 


138 


REFLECTION COEFFICIENTS 



Figure 2. Reflection coefficient, vertical polarization, versus grazing angle. Sea water. Wavelength — S band. 


shows values greater than 0.9 up to 3 degrees. On 
three flights made with vertical polarization the points 
have fallen just slightly above the theoretical curve. 

It is planned to carry on simultaneous measure- 
ments of X- and S-band values to determine the values 
to be expected on X band and to prove or disprove the 
correlation suggested above. 

9 2 EARTH CONSTANTS IN 

THE MICROWAVE RANGE»^ 

Reflection Coefficients 

In writing a summary of the latest results, it was 
thought that the following grouping of the data 
would be useful. 

1. Determination of the electrical constants of the 
ground, sea, and fresh water. 

2. Study of ground and sea reflections under condi- 
tions encountered in actual operations. 

3. Irregular reflections or scattering. 

^By L. Goldstein, Columbia University Wave Propagation 
Group. 


Electrical Constants of the Ground, 

Sea, and Fresh Water 

To obtain reliable data on the reflection coefficient, 
dielectric constant, and conductivity of the ground 
and also of fresh and sea water, a series of radio ex- 
periments were performed^'® which gave results that 
compared fairly well with those obtained in labora- 
tory experiments. The experimental conditions were 
relatively well deflned and the physical characteristics 
of the ground or water derived from these experiments 
appear to be highly reliable. The wavelengths of the 
radiation used in these experiments lie in the S band 
at 9 and 10 cm. 

In the experiments with 9-cm waves,^'^ the nature 
of the reflecting surface was prepared beforehand and 
its humidity, occasionally, well controlled. Similarly, 
with vegetation on the ground, the reflection could be 
measured with different heights of the turf which was 
grown on the grounds reserved for the measurements. 

The conditions of the ground in the experiments 
with 10-cm waves were somewhat less well defined. 


EARTH CONSTANTS IN THE MICROWAVE RANGE 


139 


However, the experimental setup was portable in 
this case, which proved to be advantageous. 

It seems desirable to give first the results obtained 
under the best-defined conditions^’ ^ (9 cm) for a 
variety of grounds and compare those with the re- 
sults of the 10-cm waves obtained under less well- 
defined conditions.® The latter results are given al- 
ways in graphical form. 

The grazing angle interval (0° to about 30°) ex- 
plored with the 10-cm waves was quite large, and a 
graphical representation of the results is well justi- 
fied. At 9 cm only three or at most four angles of in- 
cidence were investigated. 

The schematic representation of the experimental 
setup is given in Figure 3. If p denotes the ratio of 



the amplitude of the refiected wave to that of the 
incident wave in the vicinity of the reflecting sur- 
face, then at the position of the receiver the total field 
received in case of reinforcement is 


Emax = E -{■ kpE. 

E is the field strength of the direct wave and ^ is a 
correction factor taking into account the directivity 
of the transmitter and receiver as well as the increased 
path length of the refiected ray as compared to that 
of the direct ray. In case of phase opposition 


Emin — E kpE. 

These lead to 


p' = kp = 


{Emax / -^min) 1 

{Emax / Emin) + 1 


Throughout the work at 10 cm this corrected reflec- 
tion coefficient (kp) or p' has been investigated. Pre- 
sumably k is nearly unity so that p = p. 

Very Dry Sandy Ground. Table 1, for 9 cm, refers 
to very dry ground. In order to obtain a precise value 


of the complex dielectric constant of this very dry 
sandy ground its absorption coefficient was measured 
directly. The measurement was made by interposing 
a filled container between transmitter and receiver. 

Table 1. Reflection coefficients of very dry sandy ground 
for X = 9 cm.i>2 


Grazing 

angle Vertical polarization Horizontal polarization 

degrees Calculated Observed Calculated Observed 


22 

0.18 

0.20 

0.48 

0.47 

36.5 

0.015 

0.03 

0.33 

0.33 

46.5 

0.08 

0.09 

0.26 

0.27 


The container, a wooden trough, had ^/4 in. plate 
glass ends, 18 in. square, one of which was movable, 
thus allowing a test of the absorber up to a thickness 
of 12 in. The most suitable values of cr (real part 
of the complex dielectric constant cc) and conductivity 
(7 or ci = 60 (t\ (imaginary part of the complex 
dielectric constant) which fit the reflection and ab- 
sorption coefficient data were found to be cr = 2, a 
= 0.033 mho per meter, a = 0.18. 

It should be mentioned here that the calculated 
reflection coefficients were obtained by using the gen- 
eralized Fresnel formulas for reflection of electro- 
magnetic waves by plane dielectric surfaces. The in- 
cident waves travel in vacuum (or air) and fall on 
the plane surface of a dielectric at the grazing angle 
The complex dielectric constant Cc is 


€c=€r — jeiy 

= €r — j 60 <t\ , 

where cr is the real part of the dielectric constant and 
€i = 60o-X is its imaginary part, or is the conductivity 
of the dielectric medium in mhos per m, and A is the 
wavelength, in vacuum, of the incident radiation. 
The generalized Fresnel formulas, for horizontally 
and vertically polarized waves, respectively, are 



(horizontal) 

sin + (cc ~ cos^ i/')* 


^ €cSin^ — (6c— CQS^ xj/)^ 

€c sin ^ -j- ( €c— cos^ yj/ )* 


(vertical), 


where p denotes the magnitude of the complex reflec- 
tion coefficient and ^ is the angle of lag of the 
reflected component behind the incident component 
of the electric field. 

The results at 10 cm and for dry sand are given 
in Figure 4. The theoretical curves given on the 


140 


REFLECTION COEFFICIENTS 



Figure 4. Reflection coefficient p' versus X=10 cm. d = 225, 100, 75 ft. 

same as those given in the preceding case, that is, 
for €r = 4 and o- = 0. It will be noted that the tit 
with the experimental values is less satisfactory in 
this case. The author .attributes the discrepancy be- 
tween the observed and computed values of the re- 
flection coefficient, in part, to the quality of the soil 
which consisted of lumps of about a half wavelength 
diameter. In general the roughness of the ground con- 
tributes considerably to scattering. It is rather to be 
expected that a theoretical curve representing specular 
reflection coefficients from a smooth surface should 
not fit well the experimental data referring to such 
a rough ground. 

Saturated Ground. Table 2 represents the results 
obtained at 9 cm for the reflection coefficient of sat- 
urated ground. 

The most suitable values of and o- or a to fit both 
reflection and absorption measurements are = 24, 
o- = 0.66 mhos per meter, and €i = 3.56. 

Tests carried out at 10 cm on ground of somewhat 
similar type (tidal flat and moist sand) are given in 

Table 2. Reflection coefficients of saturated ground. X = 9 cm.b^ 


Vertical polarization Horizontal polarization 

^ i 


Grazing 

r 

Calculated 

A 

... 

Observed 

A 

Calculated 

Observed 

angle 

€r = 24 

6r = 25 

Heavy 

Watered 

€r = 24 

€r = 25 

Heavy 

Watered 

degrees 

<7 = 0.66 

(7 = 0 

rain 

by hose 

<7 = 0.66 

( 7=0 

rain 

by hose 

22 

0.31 

0.31 

0.28 

0.32 

0.85 

0.86 

0.90 

0.86 

36.5 

0.50 

0.50 

0.50 

0.50 

0.78 

0.79 


0.78 

46.5 

0.57 

0.57 

0.58 

0.58 

0.74 

0.75 

0.72 

0.74 


graph do not necessarily represent the best fit. These 
curves were computed for cr = 4 and o- = 0 (perfect 
dielectric). The experimental Brewster angle turns 
out to be around 23° (grazing angle). 

The experimental results for clay-sand soil are 
given in Figure 5. The theoretical curves are the 



Figure 5. Reflection coefficient p' versus i/'. X= 10 cm. 
d=100, 300 ft. 


141 


EARTH CONSTANTS IN THE MICROWAVE RANGE 



Figure 6. Reflection coefficient p' versus X= 10 cm. 
d = 90 ft. 



Figure 7. Reflection coefficient p' versus X= 10 cm. 
d = 300, 90 ft. 


Figures 6 and 7. The theoretical curves in Figure 6 
correspond to a perfect dielectric (o- = 0) with cr = 
10. Since the conductivity of the soil is not zero, the 
true value of the reflection coefficient for vertical 
polarization cannot be zero at the Brewster angle. 
The data seem to confirm this point. 

The data of Figure 7 refer to moist and very smooth 
beach sand. It is thought that these observations are 
the most reliable so far as self-consistency is con- 
cerned. Again the computed curves refer to a perfect 
dielectric with €r = 15. 

An important difference between the measurements 
at 9 cm at a fixed location and those made at 10 cm 
with the portable setup consists of the fact that at 9 
cm direct absorption measurements could be per- 
formed in addition to measurements of the reflection 
coefficent. The electrical constants could thus be deter- 
mined at 9 cm without ambiguity. 


Fresh ^Yater and Jf.^o Salt Solution (or Sea Water). 
(1) Tap water. Table 3 gives the results on the reflec- 
tion coefficients of tap water (temperature not given). 

Table 3. Reflection coefficients of tap water. X = 9 crn.^j^ 
Grazing 

angle Vertical polarization Horizontal polarization 

degrees Calculated Observed Calculated Observed 


20 

0.51 

0.51 

0.92 

0.90 

35 

0.69 

0.67 

0.88 

0.88 

45.5 

0.73 

0.70 

0.85 

0.83 


The values of cr and ei which best represent both the 
reflection and absorption data are cr = 80, o- = 2.2 
mhos per m, and ci = 11.9. 

2. Fresh ivater pond. The results on 10-cm waves 
are collected in Figure 8.^ These data refer to a fresh 
water pond and the theoretical curve corresponds to 
a smooth and perfect dielectric surface with cr — 80. 
The curves do not fit too well at the smaller grazing 
angles. If the conductivity were taken into account, 



Figure 8. Reflection coefficient p' versus r/'. X=10 cm. 
d = 90, 225 ft. Fresh water pond. 


presumably a better flt might be achieved. Two points, 
marked Ford,^’^ taken from Table 3 were included 
for comparison. 

3. Salt solution. In order to simulate sea water a 
4 per cent salt solution was used for the determination 
of the reflection coefficient. At 9 cm the best fit was 
obtained with cr — 80, o- = 6.1 mhos per m, and 

= 33. 

4. Sea water. Figure 9 gives the results obtained 
at 10 cm. The computed curves drawn to fit the data 
correspond to 6r = 69, o- = 6.5 mhos per m, cf = 39. 
It appears that the data can be fitted with the com- 


142 


REFLECTION COEFFICIENTS 



Figure 9. Reflection coefficient p' versus \p. X= 10 cm. 
d=130 ft. Sea water (tidal canal). 


puted curves as long as the ripples on the tidal canal 
are of small amplitude (about 1 in.). 

Figure 10, which also refers to sea reflection, cor- 
responds to ripples which had an amplitude of about 
2 in., and here the observed reflection coefficients for 
vertical polarization fall well below the computed 
curve at the larger values of grazing angle. Probably 
the choice of the dielectric constants used in the com- 
putations may account for at least a part of the dis- 
crepancy. 

Grass-Covered Ground. The following results ob- 
tained at the experimental grounds^’- with 9-cm waves 
refer to various types of grass-covered earth. 

The results obtained with the portable 10-cm set 
appear on Figures 11, 12, 13, and 14. These graphs 



show clearly the influence of vegetation on the re- 
flection coefficient. Consult Table 5 for corresponding 
results at 9 cm. 


0.8 


H 0.6 

z 

o 

u. 

u. 

UJ 

8 0.4 

z 

o 

u 

u 

uJ 0.2 

UJ 

a: 


0 

0 4 8 12 16 

GRAZING ANGLE IN DEGREES ^ 

Figure 11. Reflection coefficient p versus X=10cm. 
d=225 ft. Grass covered ground. 


u~ 

X 

o 

X 

* 




< 

o 

X 

X 

o 

X 


O VERl 
— X HORI 

PLACE 

EARTH 

1 

nCAL POLi 
ZONTAL P( 

-HICKSVILI 
- ROLLING 
GRASS 4 

1 1 

o 

^RIZATION 

3LARIZATIC 

LE AIRPOl 
FIELD, S( 
" LONG 

1 

>N 

RT 

DIL DRY, 

1 


1.0 


0.8 


It 0.6 


z 

o 

i= 0.4 


0.2 





o VER‘ 
« HORI 

nCAL POL 
IZONTAL P 

PERRY "BA 
LIGHTLY R 
4"' 18“ HIGI 

ARIZATION 

OLARIZATI 

CKYARD" 
tOLLING, G 
H, DRY 

ION 




PLACE'S 

EARTH'S 

RASS 


X 

I 

* X 

X 





« 



X 

X 

o 

o 

® ® o 

o 

o 

o 

o 

<?o °° 

® o 

o 

o 

o 

oo 


8 12 16 20 
GRAZING angle IN DEGREES 'p 


24 


26 


Figure 12. Reflection coefficient p versus X= 10 cm. 
d= 100, 225 ft. Grass covered ground. 





O VERTICAL POLARIZATION 
» HORIZONTAL POLARIZATION 




PLACE- 

EARTH- 

NY STATE 
■BEET FIEl 

AG INST 
.0 WITH Wl 

BEDS 









o 

X 

1 

o 

o ^ 

X 

X 

X 

oO 


K 

K 


qI 1 

0 4 8 12 16 20 24 28 

GRAZING ANGLE IN DEGREES i 



Figure 10. Reflection coefficient p' versus X=10cm. 
d=90 ft. Sea water. 


Figure 13. Reflection coefficient p versus X= 10 cm. 
d=100 ft. Beet field with weeds. 


EARTH CONSTANTS IN THE MICROWAVE RANGE 


143 


Table 4. Reflection coefficient of level, grass-covered ground. X = 9 cm. Grazing angle 10°. 


Ground conditions 

Vertical polarization 
Calculated Observed 

Assumed constants 
€r <7 mhos/m 

Horizontal polarization 
Calculated Observed 

Grass cut very short and rolled dry. 

(No rain for at least 7 days.) 

0.47 

0.46 

3 

0.055 

1 

0.79 

0.79 

Cut very short and rolled wet. 

(Several hours of rain on previous night.) 

0.36 

0.37 

6 

0.11 

0.86 

0.86 

Grass about 1 in. high, wet. 

(Same day as previous test.) 

0.36 

0.51 

6 

0.11 

0.86 

0.83 


Table 5 . Magnitudes p, and p*, observed values. 

X = 

9 cm.b2 





Height of 



Grazing angle 




vegetation. 

22 

o 

36 

.5° 

56 

.5° 

Appearance of ground 

cm 

V 

h 

V 


V 

h 

Bare 

0 

0.32 

0.86 

0.50 

0.78 

0.58 

0.74 

True leaves beginning to form, ground visible 

3-4 

0.40 

0.50 

0.44 

0.55 

0.47 

0.56 

Dense clumps, ground showing in places 

9-12 

0.18 

0.65 

0.23 

0.58 

0.33 

0.49 

Ground almost obscured 

20-25 

0.06 

0.32 

0.10 

0.39 

0.17 

0.41 

Ground completely obscured 

35-45 

0.04 

0.19 

0.05 

0.26 

0.11 

0.28 




Table 6 . 

Reflection coefficient of rough ground. X = 

9 cm.b2 



Grazing 

angle, 

degrees 

Level 

estimated 

Vertical polarization 
Long Short 

grass grass 

Bare 

Level 

estimated 

Horizontal polarization 
Long Short 

grass grass 

Bare 

22 

0.20 

0.08 

0.20 

0.23 

0.82 

0.12 

0.74 

0.81 

36.5 

0.40 

0.06 

0.17 

0.27 

0.73 

0.12 

0.43 

0.50 

46.5 

0.48 

0.06 

0.16 

0.26 

0.68 

0.03 

0.36 

0.46 


0.8 

<». 

I 0-6 

O 
U. 

U. 

UJ 

o 0.4 

z 

o 

S 0.2 

-I 
li. 

(ij 

tr. 

0 

0 4 8 12 16 20 24 26 

GRAZING ANGLE IN DEGREES ^ 

Figure 14. Reflection coefficient p versus \f/. X=10 cm. 
d= 102, 200 ft. Trees, bushes, weeds in gravelly soil. 




1 

o VE 
X HO 

RTICAL POLARIZATION 

RIZONTAL POLARIZATION 

E - N Y STATE AG INST 

H- PINE TREES 3'-10' TALL, 

BUSHES, WEEDS IN GRAVELLY 



PL AC 
EART 



o 

SOIL 



o 


1 ^ 

X 

’ 0 

«, . 0 



X 

X 

‘ 


then remeasured with the grass mown as short as the 
roughness of the ground permitted. The turf was next 
removed, some of the irregularities of the ground were 
eliminated, and the reflection coefficient of the sur- 
face so prepared was measured again. The results of 
these measurements are to be found in Table 6. The 
estimated reflection coefficient of level ground of the 
same moisture content is also included here. 

Finally, the results on the electrical constants of 
different kinds of grounds for 9-cm waves have been 
collected in Table 7. 

Table 7 . Electrical constants of the ground. X = 9 cm.b 2 


Since, however, the data of Table 5 refer to wet 
vegetation-covered ground, they cannot be compared 
directly with the results at 10 cm since these seem to 
correspond to dry vegetation. 

Table 6 gives the data obtained at 9 cm for un- 
mown meadow land having an average variation in 
ground level of about 7 cm. The ground was covered 
with a dense layer of grass about 30 cm high. The 
reflection coefficient of this surface was measured. 


Attenuation 


Medium 

€r 

<r mhos/m 


factor db/m 

Very dry sandy loam 

2 

0.033 

0.178 

36 

Saturated sandy loam 24 

0.666 

3.54 

220 

Tap water 

4% solution of coarse 

80 

2.22 

12.0 

380 

salt 

80 

6.11 

33.0 

1100 

Dry turf 

3 

0.055 

(est) 

0.30 

50 (calc) 

Wet turf 

6 

0.11 

(est) 

0.60 

80 (calc) 


144 


REFLECTION COEFFICIENTS 



Figure 15. Cross section of Forth Gain Bay (Wales) in vertical plane through transmitter and receiver. 


It is seen that in the previous experiments^*^ no 
attempt was made at finding the phase angle shift at 
reflection. At 10 cm^ such an attempt was made. How- 
ever, the distances involved here could not be meas- 
ured more accurately than a small fraction of a half 
wavelength, or 5 cm. Therefore, these experiments 
are not to be considered, as the author himself points 
out, as giving quantitative information on the phase 
angle shift at reflection and they will not be dis- 
cussed here. 



Figure 16. Sea reflection coefficient Pf versus grazing 
angle yp at 10 cm. Vertical polarization. 


Summary of Experimental 
Investigations on Reflection 

Here the results of certain additional reports of 
experiments on microwave reflection by either sea or 
land performed under more nearly operational con- 
ditions are summarized.^''^ 

In one series of experiments^ performed by British 
workers, at 9.3 cm, the transmitter was located on the 
shore and could be placed at two heights, 35 and 130 








•• . * 
• •<** • 

i • • • 

•tf * *• 

• • 



• •• . 

'•V ’ 

V.. ;• 

• * 

• • • 

• • • • 

• 

• H 



• 

• 

• • 

• ^ 

’*•*** , • 

• ; •* 



• •* 

• • 

• • 

• 

• • 







• ••• 

































0 1 2 3 4 5 6 

GRAZING ANGLE IN DEGREES 


Figure 17. Sea reflection coefficient P* versus grazing 
angle \p at 10 cm. Horizontal polarization. 


EARTH CONSTANTS IN THE MICROWAVE RANGE 


145 


ft. The receiver was placed on a ship at a constant 
height of about 33 ft. The field strength of the radia- 
tion was measured as a function of the distance from 
the transmitter. This distance varied between 3,500 
and 42,000 yd. The observed values of the field 
strengths correspond well with calculations based on 
electromagnetic theory. 

In a second series of experiments^ both the trans- 
mitter and receiver were stationary. The topography 
of the location and the experimental setup are rep- 
resented schematically in Figure 15. The main con- 
clusion drawn from these experiments was that even 
for a calm sea (vertical amplitude of the waves less 
than 8 in.) the mean amplitude of the reflected ver- 
tically polarized beam was only about half the steady 
amplitude of the direct wave. The amplitude of the 
reflected wave, however, occasionally rises to greater 
values than that of the direct wave, but this lasts only 



0RAZIN6 ANGLE IN DEGREES 

Figure 18. Sea reflection coefficient P*, versus grazing 
angle ^ at 3.2 cm. Vertical polarization. 


for short lengths of time of the order of 0.5 sec. 

Ill the case of the reflection of horizontally polar- 
ized radiation at the surface of a smooth sea it is 
known that even for grazing angles as large as 10° 
the amplitude of the reflected wave is very nearly equal 
to that of the direct wave. The irregularities of the 
sea, however, reduce the amplitude of the refleeted 
wave. This reduction is due to scattering, i.e., to non- 
specular reflection of the radiation by the irregu- 
larities of the sea surfaee. It is recalled here that the 
surface irregularities will play an important role as 
soon as they are larger than X/k(/, A being the wave- 
length and if/ the grazing angle in radians. 

The Eadiation Laboratory workers,®’’' used an air- 
plane as the carrier of the receiver flying toward the 
transmitter. For 10- and 3.2-cm waves the latest re- 
sults are given in Figures 16, 17, 18, and 19. These 
show that theory and experiment check satisfactorily 
for vertical polarization, but for horizontal polariza- 



GRAZING ANGLE IN DEGREES 


Figure 19. Sea reflection coefficient Pn versus grazing 
angle ^ at 3.2 cm. Horizontal polarization. 


146 


REFLECTION COEFFICIENTS 


tion the experimental values of reflection coefficient 
generally fall well below the theoretical values based 
on the assumption of a smooth sea. Whereas over sea 
a regular interference pattern existed, over land 
(Orlando, Florida) no specular reflection was ob- 
served. The lobe structure was absent in the observa- 
tions over land. 

Another experiment® carried out over land was 
performed using X-band waves between BeeFs Hill 
and Deal, New Jersey. The reflection coefficient of 
the ground is expected to change with the seasons 
on account of seasonal vegetation changes on the path. 
One series of measurements lead to reflection coeffi- 
cients of 0.17 and 0.20 for horizontally and vertically 
polarized radiation respectively. 

Specular Reflection and Scattering 

Ordinarily neither the sea nor the land are ideally 
smooth, and one would expect always nonspecular re- 
flections which tend to perturb the interference pat- 
tern of the direct and reflected rays from a smooth 
surface. 

It has been pointed out® that the condition which 
has to be fulfilled for specular reflection to occur is 
that the grazing angle x}/ be such that sin \j/ ^ X/g, 
where g is the wavelength of the sea waves. Clearly 
this is a kind of limiting condition and assumes the 
perfect regularity of the sea waves. It is seen that 
the above condition expresses the fact that the smaller 
the grazing angle, the smaller are the apparent irregu- 
larities of the sea and, if these apparent irregularities 
are much closer than the wavelength of the incident 
radiation, it is to be expected that specular reflec- 
tion should predominate. 

A direct consequence of this condition is that the 
echoes from a target, that is, a ship, will not be 
drowned by the clutter from the sea waves for large 
distances between the target and observer. Whereas at 
closer distances (large grazing angles) the echo from 
the target might be drowned by the irregular reflec- 
tion, i.e., scattering from the sea. To this effect, a report 
is quoted in which it is stated that ships could only 
be detected beyond a certain distance from the shore. 

It is also thought^® that the discrepancies observed 
between the theoretically predicted and measured sea 
reflection coefficients (horizontal polarization) could 
be attributed to scattering. The irregular reflections 
have the effect of decreasing considerably the ratio of 
the successive maxima and minima of the interference 
pattern developed. The discrepancies referred to are 


those discussed by the Iladiatioii Laboratory workers.^ 
Ill this connection, Eckersley mentions some experi- 
ments by Hoyle on sea reflections in which no corre- 
lation could be observed on the voltage registered by 
two aerials a few inches apart. This tends also to sug- 
gest the existence of scattering from the sea. 

In another series of transmission experiments^® it 
was observed that the contrast between maxima and 
minima was poor. Here the experiments were carried 
out at 200 me over sea at a distance of 100 miles be- 
tween an airplane and a ground station. The diver- 
gence of the observed from the calculated values of 
reflection increases as the grazing angle increases. 
This seems to be in agreement with the results accord- 
ing to which the sea surface may be considered as 
formed by a number of corrugations which, for small 
grazing angles, appear to be so close together that the 
reflection is mostly specular. 

As to the frequency variation of scattering one 
would expect more and more scattering with increas- 
ing frequency. 

The effect of uneven ground on the reflection co- 
efficient was investigated by the British workers al- 
ready mentioned.^’® The reflecting ground consisted 
of an artificially prepared series of uniform ridges, 
placed along, across, and at 45° to, the direction of 
propagation. These ridges simulated waves, and their 
wavelength D lay between 0.6 and 1.2 m, whereas the 
double amplitude li varied between 5 and 15 cm, and 
the wavelength of the radiation used was 9 cm. 

Tables 8 and 9 giA^e the reflection coefficients of 
the uneven ground when the direction of propagation 
is at 45° with the ridge and along or across the ridge 
system. The tables also give an estimation of the re- 
flection coefficient of level ground of the same moisture 
content as that under test. 

The results given in these tables show how a rela- 
tively small irregularity in the ground surface is 
sufficient to prevent regular reflection. The reflection 
coefficient becomes erratic when it has fallen below 
a value of about 0.1. The values given for level ground 
refer only very approximately to the state of the 
ground in the ridged condition. Since the measure- 
ments extended over several days, those relative to 
level ground may not correspond necessarily to the 
same degree of moisture as those referring to the 
ridged ground. The level reflection coefficients in the 
two preceding tables differ from each other because 
those of Table 8 refer to drier ground than those of 
Table 9. 


MEASUREMENTS OF THE REFLECTION COEFFICIENT OF LAND 


147 


Table 8. Reflection coefficient of ground ridged at 45® with the direction of transmission. X = 9 cm.h^ 


Grazing 

angle, 

degrees 

Level 

estimate 

Vertical polarization 

D = 60 cm D = 120 cm 

A = 14 cm h = 10 cm 

D = 120 cm 
h = 5 cm 

Level 

estimate 

Horizontal polarization 
D = 60 cm i) = 120 cm 

A = 14 cm h = 10 cm 

D = 120 cm 
h = 5 cm 

22 

0.08 

0.07 

0.09 

0.13 

0.65 

0.14 

0.18 

0.30 

36.5 

0.13 

0.04 

0.05 

0.07 

0.51 

0.04 

0.06 

0.16 

46.5 

0.22 

0.04 

0.04 

0.04 

0.45 

0.07 

0.06 

0.10 


Table 9. 


Reflection coefficient of ground ridged along or across the direction of transmission. 


X = 9 cm. 




Vertical polarization 




Horizontal polarization 



Grazing 


Along 

Across 



Along 

Across 


angle. 

Level 

D = 60 cm 

D = 60 cm 

D 

= 120 cm 

Level 

D = 60 cm 

D = 60 cm 

D 

= 120 cm 

degrees 

estimate 

h = 14 cm 

^ = 16 cm 

h 

= 12 cm 

estimate 

A = 14 cm 

h = IQ cm 

h 

= 12 cm 

12 

0.23 

0.20 

0.10 


0.30 

0.86 

0.4 

0.2 


0.4 

22 

0.06 

0.03 

0.05 


0.12 

0.76 

0.07 

0.10 


0.18 

36.5 

0.28 

0.03 

0.02 


0.06 

0.64 

0.10 

0.12 


0.16 

46.5 

0.36 

0.04 

0.08 


0.08 

0.58 

0.04 

0.08 


0.14 


9 3 MEASUREMENTS OF THE REFLECTION 
COEFFICIENT OF LAND AT CENTI- 
METER WAVELENGTHS, CARRIED 
OUT AT NATIONAL PHYSICAL 
LABORATORY® 

Experiments have been made on the reflection and 
absorption of radio waves in the S-band of wavelengths 
by workers in the National Physical Laboratory in 
England. The reflection coefficient has been measured 
at angles of incidence to the vertical, of 80°, 68°, 54°, 
and 44° on level ground, fresh water, sea water, uneven 
ground, ground covered with vegetation, and ground 
covered with ^ in. mesh wire netting. The absorption 
in soil, fresh water, sea water, and V 2 in. mesh wire net- 
ting has also been measured by a laboratory method. An 
interim report^ gave some of the salient results 
obtained on ground reflection. 

The main conclusions which have been drawn from 
the results obtained are given below. 

1. Specular reflection can be obtained only from a 
very level surface, with little or no vegetation on it. 
The electrical constants of such surfaces are given in 
Table 10, from which the coefficient of specular reflec- 
tion can be deduced for the angle of incidence and 
state of polarization concerned. 

®By W. Ross, British Central Scientific Office, Washington, 

D. C. 


2. The reflection coefficient decreases with uneven 
ground and is reduced to a value of about 0.2 by in- 
equalities of level of about one wavelength. This con- 
clusion is based mainly on a series of experiments in 
which the ground was raked into a series of ridges 
resembling waves, which could be either in, across, or 
at an angle to, the direction of transmission. Similar 
results were obtained when a large sheet of wire net- 
ting was similarly disposed in a series of waves. 

3. Vegetation reduces the reflection coefficient, in 
general, and when about 2 ft high causes a reduction 
in reflection coefficient to a value of about 0.2, An in- 
teresting exception was found when level ground was 
covered with vegetation less than half a wavelength 
high (about 1^ in.) when the reflection coefficient 
with vertical polarization increased slightly with high 
angles of incidence over that obtained with level 
ground. 

Table 10 


Dielectric Conductivity 

Nature of surface constant mhos / m 


Bare sandy loam, very dry 

2 

3 X 10-2 

Bare sandy loam, saturated with water 

24 

6 X 10-1 

Turf with grass very short (cricket 



wicket), dry 

3 

5 X 10-2 

Turf with grass very short (cricket 



wicket), wet 

6 

1 X 10-1 

Fresh water 

80 

2 

Sea water (4% salt solution) 

80 

5 


Chapter 10 

DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


10 1 ABSORPTION AND SCATTERING OF 
MICROWAVES BY THE ATMOSPHERE- 

T he present report deals with the absorption of 
microwaves in the 0.2- to 100-cm wavelength range, 
by the atmospheric gases and by floating or falling 
water drops like clouds, fog, and rain of maximum 
drop diameter 0.55 cm. 

The theory of absorption and scattering of waves 
by spherical particles is briefly reviewed. The results 
are applied to water drops. 

For small drops, the attenuation, which depends 
only upon the amount of liquid water per unit volume 
and is independent of the drop size, is 0.28, 0.049, and 
0.0045 db per kilometer for each gram of liquid water 
per cubic meter of air for the K, X, and S bands, re- 
spectively. Since the concentration of liquid water in 
clouds does not seem to exceed 4 g per cubic meter of 
air, the above values represent upper limits. These 
values refer to water droplets at temperatures around 
18 C. The attenuation increases with decreasing tem- 
perature of the water drops. 

While the attenuation does not depend upon the 
total rate of rainfall, it is possible to calculate the 
maximum values to be expected for any precipitation 
rate. These are 0.16, 0.45, 0.005, 0.001, and 0.0006 db 
per kilometer for each millimeter precipitation per 
hour at 1.25, 3, 5, 8, and 10 cm, respectively. These 
theoretical maximum values of attenuation compare 
fairly well with the values observed and are for water 
drops at 18 C. 

In the wavelength range mentioned it is shown that, 
with the exception of the biggest drops and shortest 
waves, the wave energy converted into heat inside the 
drops is much larger than the scattered energy. 

The radar absorption coefficient, deflned as the frac- 
tion of the incident power scattered backward per unit 
layer thickness of the echoing medium, has been com- 
puted for different rains. This allows the estimation of 
the power received in radar observations of storm clouds 
and rains. The theoretical predictions seem to be con- 
sistent here also with the results of the few recent radar 
studies which tend to show that echoes are due mainly 
to water drops of the dimensions occurring in rains. 

*By L. Goldstein, Columbia University Wave Propagation 
Group. 


In the introduction a resume is given of the status 
of microwave absorption by atmospheric oxygen and 
water vapor. With the exception of the resonance re- 
gion of oxygen (resonance wavelength around 0.5 cm), 
this absorption turns out to be of only very limited 
practical importance for waves longer than about 3 to 
5 cm. 

Introduction 

The present report is intended to review the status 
of microwave propagation through rain, clouds, and 
fog. In order, however, to convey a precise idea of the 
total atmospheric absorption, we shall include here 
some of the most important numerical results recently 
obtained on the absorption of microwaves by atmos- 
pheric gases, like oxygen and water vapor.^'^ 

First of all, in medium- and low-altitude fair- 
weather clouds and fogs, with the possible exception of 
heavy sea fogs, the attenuation is of negligible impor- 
tance for longer waves. It may become important at 
shorter waves. For instance, in the K band the atten- 
uation^ is 0.28 db per kilometer for each gram of liquid 
water per cubic meter of air. The X- and S-band 
waves are attenuated, respectively, 0.049 and 0.0045 
db/km/g/nF. Since in these clouds and ordinary fogs 
the liquid water concentration does not seem to exceed 
1 g/m®, these valnes are very likely upper limits. Actu- 
ally, by halving these numbers one would be nearer the 
true values, inasmuch as liquid water contents reported 
in clouds®’® varies between 0.15 and 0.50 g/m®. An in- 
teresting and simplifying feature of cloud and fog 
absorption is the fact that the smallness of their 
water drops, as compared with the wavelength, makes 
the attenuation independent of the drop sizes. The 
cloud and fog attenuation depends linearly on the 
liquid water concentration of the atmosphere, and in 
the microwave region it decreases monotonically with 
increasing wavelength. 

In rains or rain clouds the attenuation does not 
depend directly on the total rate of rainfall, a variable 
so familiar to meteorologists. It is, nevertheless, pos- 
sible to give upper limits to the attenuation per unit 
precipitation rate. These are as follows: 0.16, 0.45, 
0.005, 0.001, and 0.0006 db per kilometer for each mil- 

•’The attenuation values given in this report are always for 
one-way transmission. 


148 


ATMOSPHERIC ABSORPTION AND SCATTERING 


149 


limeter per hour rate of rainfall, at 1..25-, 3-, 5-, 8-, and 
10-ein wavelengths, respectively. The drops forming 
these rains were supposed to be at temperatures near 
18 C. By increasing the preceding values by about 30 
per cent one would very likely take care of raindrops at 
lower temperatures, since the absorption increases 
with decreasing temperature of the drops. 

In the computation of attenuation for rains it was 
assumed that ideal conditions prevailed throughout the 
rains under consideration. By this was meant that the 
same sample of rain falling, say, over an area of 1 sq m 
woidd be found anywhere inside the area covered by 
the rain. Such ideal rains seem to be rather simple 
theoretical models. Considerable fluctuations in the 
rate of rainfall over relatively short distances (1 km 



3.0 6.0 9.0 15 30 60 90 150 


FREQUENCY IN 10^ MC ► 

I I I I I I I I I I I I 

10 5 4 3 2 1.5 1 0.8 0.5 0.4 a3 0.2 

X IN CM 

Figure 1. Oxygen and water vapor absorption versus 
wavelength. (1) Absorption due to water vapor in an 
atmosphere at 76-cm pressure containing 1 per cent 
water molecules, or 7.5 g per cu m. The water resonance 
line is assumed to be at 24,000 me, and its half-width at 
half maximum (line breadth) is 3,000 me. (2) Absorp- 
tion due to oxygen in an atmosphere at 76-cm pressure, 
whose resonance band at 60 • 10^ me is supposed to have 
a line breadth of 600 me. 


or less) have been reported.^® These spatial irregular- 
ities of rains exclude any simple interpretation of the 
experimental data on rain attenuations. The computed 
values of attenuation are based on a few data on drop 
size distributions^^ in rains. 

In Figure 1,^ the individual oxygen and water 
vapor attenuation curves have been plotted in the 0.2- 
to 10-cm wavelength range, using the most acceptable 
data available on the position of line centers and line 
widths. Any change in the water vapor content from 
the one adopted for this graph (7.5 g/m^ of air or 6.2 
g per kilogram of air) or the total pressure can be 
taken rapidly into account in computing the combined 
oxygen and water vapor attenuations, since the atten- 
uation values are proportional to the partial pressures 
of oxygen and water vapor. For practical purposes the 
effect of atmospheric temperature variations can be 
neglected. 

In Figure 2 is plotted the total (oxygen plus water 
vapor) attenuation (curve 1) in an atmosphere at 
76-cm pressure with the same water vapor content 
as the water curve of Figure 1. Curves 2, 3, and 4 are 
rain attenuation curves computed for a moderate rain 
(rate of rainfall 6mm per hour), a heavy rain (22mm 
per hour), and an excessive rain of cloud burst pro- 
portion (43 mm per hour). The corresponding drop 
size distributions were given by Best.^^ 

In any rain the resulting total attenuation is the 
sum of the gaseous (oxygen plus water vapor) and 
corpuscle or liquid drop attenuation values. 

It is thus seen that for waves of 3 cm or shorter the 
rain attenuation may become prohibitive, whereas the 
gaseous attenuation loses its practical importance at 
waves longer than about 2 cm. The attenuation of rain 
computed in this report extends from 5 cm toward 
longer waves. In the region X = 1.25 — 5 cm, only 
tAvo attenuation values are available,^^ at 1.25 and 3 
cm respectively. The dashed portions of the rain atten- 
uation curves are thus extrapolations drawn through 
the two computed points. The shape of these extra- 
polated portions of the curves, in view of the decreas- 
ing trend of the computed dielectric absorption values 
with the wavelength,^^ seems to suggest that the rain 
attenuation might level off or even decrease for waves 
shorter than 1 cm. However, without a closer inves- 
tigation of the raindrop absorption in this wavelength 
region, no precise statement can be made on this 
subject. 

As regards the normal atmospheric absorption of 
microwaves, it may be mentioned that the oxygen ab- 


150 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 



150 90 50 30 24 15 10 6.0 3.0 1.5 1.0 0.6 0.3 

FREQUENCY IN 10^ MC 


m — rn — n — i — ^ — i—rn — n — i — ^ 1 

0.2 03 0.7 1.25 2 3 5 7 10 15 20 30 50 100 

A IN CM ► 

Figure 2. Atmospheric attenuation for one-way trans- 
mission. (1) Oxygen and water vapor (total p = 76 cm 
Hg, i=20 C, water vapor=7.5 g per cu m). (Van 
Vleck). (2) Moderate rain (^6 mm per hr) of known drop 
size distribution. (3) Heavy rain (22 mm per hr). (4) 
Rain of cloudburst proportion (43 mm per hr). 

sorption is due to the paramagnetic character of this 
gas. It is through the interaction of the magnetic field 
strength with the magnetic dipole moment of the oxy- 
gen molecule that microwaves are absorbed by this 
gas. In the microwave region the oxygen molecule has 
a resonance line at A = 0.25 cm and a band near 0.5 
cm, while water vapor seems to have a resonance line 
around 1.25 cm and interacts with the radiation field 
through its electric dipole moment. The whole subject 
has been discussed exhaustively.^*^ 

The study of the scattering of microwaves by rain- 
drops shows that the radar observations of rainclouds 
can be explained satisfactorily if the scattering is at- 
tributed to spherical particles of dimensions similar 
to those of raindrops, even though no rain reaches the 
ground. Recent experimental work^^*^® has helped 
considerably in clearing up the apparent inconsist- 
ency which previously existed in this subject. 


On the whole, taking into consideration the irregu- 
larities of the precipitation forms in space, it may be 
said that theory provides a fairly good picture of mi- 
crowave propagation through a cloudy, foggy, or rainy 
atmosphere. 

The major object of the present paper is to report 
the theoretical and experimental work done on atten- 
uation of microwaves by liquid or solid water particles 
falling through the atmosphere, as well as clouds and 
fog, which are water and ice particles in suspension. 

Theoretical work has thus far been concerned with 
the problem of a plane electromagnetic wave scattered 
and absorbed by a single spherical or spheroidal par- 
ticle, first studied in detail by Mie^® for other purposes. 

The application of the results of Mie to very short 
radio waves propagated through rain, clouds, and fog, 
i.e., through a swarm of spherical water droplets, was 
made by Eyde.^^*^’’ The present report is, in part, an 
extension of his work using more detailed meteorologi- 
cal data on rains. 

A compact and elegant presentation of the problem 
of absorption and scattering of a plane wave by a 
sphere is given by Stratton. The method followed 
by him was first used by Lord Eayleigh.^® In the follow- 
ing section a brief review of this method will be given. 

Scattering and Absorption of Radio 
Waves by Spberical Particles 

Let the center of a sphere of radius a be the origin 
of a rectangular coordinate system and suppose a 
plane wave to be propagated along the positive z axis 
and to fall on the sphere (Figure 3). The sphere of 
permeability /Xj (henrys per meter) and complex in- 
ductive capacity ci (farads per meter) is em- 
bedded in a medium of permeability and inductive 
capacity cg. The plane wave is supposed to be polarized 
parallel to the x axis. 

The electric and magnetic field strengths Ei, Hi 
of the incident wave (subscript i) are expanded into 
spherical wave functions. The reason for this expan- 
sion lies in the boundary conditions and will appear 
clearly below. 

Ei = Ex = a:, iJo e , 

Hi = H, = L, e -'V + 

*2 

where 

k = (jLieoj^ — - jfjLcro))^ (2) 

is the complex wave number of the medium (here 
^*2 = 27r/A, A being the wavelength referred to air or 


ATMOSPHERIC ABSORPTION AND SCATTERING 


151 


free space), the scpiarc root is so taken that the imag- 
inary part is negative, and rj is the intrinsic impedance 
of the medinm, or 


ll(jd 

Y’ 



377 ohms. 


(3) 


The conductivity o- is expressed in mhos per meter; 
the frequency w, in radians per second; a-c, a^, and a« 
are unit vectors pointing in the positive x, y, and z 
directions, respectively. 

The plane wave vectors*^ a^-e'^V and 
will now be expanded into spherical wave vectors^®'^ 
at a point of spherical polar coordinates It is 

readily recalled that 

X = r sin 0 cos <f>, 
y — r sin 6 sin <f>, 

z = r cos 6y ( 4 ) 

with 


Here, I*l{x) is the first associated Legendre poly- 
nomial of the first kind ; i^, 12 , and ig are unit vectors 
drawn in the increasing r, 6, and <f) directions at the 
point on the sphere of radius r (Figure 3). 

The vectors ig and ig are tangent to the sphere along 



Figure 3. Spherical coordinates. 


0 ^ 0 ^ TT and 0 < 2 tt . 

These spherical vector waves will be denoted by m 
and n. They form complete orthogonal sets whose 
members are defined by the following equations : 

(kr) Pi (cos 0) cos (f) h 

sin 0 

— (^0^ sin (t> is, 

(10 

= (kv) PI (cOS 0) SIR 0 is 

Sin 0 

dP^ 

— (kr) — ^ cos <f) is , (5) 

aO 

z (kv) 

non^“^ = n (n+ 1) Pi (cos 0) sin 0 h 

lev 

1 d 

+ J r— — [vZr^^ (kr) ] Pi (cos 0) cos <t> is , 

kr sin 0 dr 

z (kv) 

= n (n+l) Pi (cos 0) cos 0 ii 

K/T 

Id , W7 XT 

1 d 

“ iYYYe Yr ^ 

“Henceforth the time factor will be omitted, as it 
does not play a direct role in what follows. 


a meridian and a parallel circle respectively. The 
superscript a takes on two values. In the expressions 
for the incident wave and the transmitted wave inside 
the scattering sphere, it has the value 1, while its 
value is 3 in the expressions for the scattered wave. 

Explicitly, 

Z^n\x) = (V2X)V„+J(X), 

(7) 

(x) = (,r/2x)*i/® j(x). 


is the Bessel function of the first kind and 
half integer order, while llf'>j^,(x) is the Hankel 
function of the second kind and half integer order. 

The expanded field strengths of the incident wave 
are then 


E.- = £o2(-j)" 44^ (“ol + in®) , 
n(n+l) 


n= 1 


H.. = - . 

1)2 ,,=1 n(n+l) 


(8) 


It is seen that the nth expansion coefficient of Ei 
into the m waves is ( — jY[(2n 1) /n(n 1)^, 
whereas the corresponding expansion coefficient into 
the n waves is( — )” • (^n l)/n(n + 1) ], etc. 

The radiation field induced by the incident radia- 
tion is composed of the transmitted radiation field 
(Eo H,) and the scattered radiation (Eg, H^) which, 
at large distances (r) from the scattering sphere, be- 
haves as a divergent spherical wave, whose amplitude 
vanishes as 1/r. 

The scattered and transmitted steady-state fields 


152 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


will now be expanded, in analogy with the incident 
field (Ei, Hi). Thus, 


-n 'V / -N + 1 

E. = ' 

n{n + 1) 




<3)' 


(9) 




(3)> 


V2 n=i n(n+l) 

valid at distances r>a, i.e., outside the sphere in 
medium 2. Clearly in equations (6) and (7), in the 
expressions of m and n, replaces k according to 
equations (5) and (6). 

Inside the sphere (complex wave number in- 
trinsic impedance the transmitted field is ex- 
panded in the following way : 


00 

E, = BoX (ai m® + X n«>), 


n{n + 1) 


( 10 ) 


E'o 'V / -N + 1 < (1) . t (i)\ 

Hi ( , 7 )” ~ ' ^ (Pn J^n ) • 

VI n=i n(n+l) 

The final determination of the scattered and trans- 
mitted fields is thus reduced to finding the coefficients 
(or amplitudes) a«, and h^. 

The preceding formulas permit one to write down 
rapidly the polar components of the different field 
strengths (Ei, H^), (Eg, H^), and (E^, H^). The 
boundary conditions at the surface of the sphere de- 
mand the continuity of the tangential components of 
the total field outside the sphere and the transmitted 
field. If we denote these tangential components by 
subscripts 6 or <f>, the boundary conditions take on 
the following form: 


4 + El = El, Hi -\-H^ = Hi, r = a. (11) 


These lead to the following systems of equations for the 
determination of the coefficients (a® , 1)\) and {a^, EJ : 

a' (Vp) - < 0® (p) = 4" (4 . (12) 

m‘n [Np 2® (iVp)] -pX ^ [p^® (p)] 
d{Np) dp 

= Mi|- (p)] , 

dp 

poiVfeUl" {Np) (p) = (p), 

4-^[iVp4*>(Vp)] 

d{Np) 

- NK Y (p)] = N^ [p^® (p)], (13) 

dp dp 

where N = p = k^a and the {x) and 

2 ? (^) ffie spherical Bessel functions defined in 


equation (7). Elimination of from the first pair 
and that of from the second pair of these equa- 
tions leads to 


^ Pizj^ {Np) [p^,® (p)]' -p,4" (p) [Arp4» (JVp)]' 

" mi4‘> {Np) [pzf> (p)]' -m23® (p) [Vpz® (iVp)]' ’ 

(14) 

^ piz®(p)[Vp4”(Vp)]'-P.v^4"(iVp)[p4‘\p)]' 

" p,z)^\p)[Npzll\Np)Y-P2Nhi»{Np) [pz® (p)]'' 
The primes at the square brackets stand for differen- 
tiation with respect to the argument of the Bessel 
function inside the brackets. Similarly, eliminating 
a® and &®, respectively, one would get and 
appearing in the field strengths inside the sphere. 

For the computation of either the scattered or ab- 
sorbed radiation, one needs to know the field strengths 
at a large distance r from the center of the sphere, 
i.e., for r a, or ^ k^a. It is important to notice in 
this connection that the coefficients an and become 
small for n > k^a, and the summation over n may 
then be limited to the integer U' — k^a. At great dis- 
tances r, > n; in other words, the order n of the 
terms of importance is less than the argument (k^r) 
of the spherical Bessel functions. Under these condi- 
tions the asymptotic expressions of these functions 
can be used. These are given by^®^ 

z\}\hr) cos (^r - 

kr 

From these asymptotic expressions one sees that the 
radial components of the scattered field strengths 
can be practically neglected; they decrease with r as 
1/r^, in contrast with the 6 and </> components which 
decrease as 1/r. This means that for large r, the field 
is transverse to the direction of propagation (radia- 
tion zone). Hence, 


El = HI = 0, r a, 


(16) 


and with 0 -^ = 0 


E 


1 = mHl =(I) i 


2ti -|- 1 

n{n + 1) 


/Pi dPi\ 

1 -T— + K —jr )cos<t>, 

\ Sin 6 de / 


E%=- Z 


2p+ 1 , (17) 


j n{n + 1) 

/ , dPi Pl \ . ^ 

\ dd sin 6 / 


ATMOSPHERIC ABSORPTION AND SCATTERING 


153 


Since the resultant field at any point outside the 
sphere is obtained by superposition of the incident 
and scattered or reflected fields, one has 

E = Ei + E,; H = Hi + H, . (18) 

In view of equation (16), the complex Poynting vector 
associated with this resultant field is radial, so that 


(19) 

where an asterisk denotes the complex conjugate. 
Using equation (18) one gets 


= h (4 + i - E% Hl^) 

+ + El Efi* - E;; hi* - El Hi*). (20) 

The first term on the right-hand side is the rate of 
flow of energy in the incident wave and the second 
term is the rate of flow in the scattered wave. The 
total scattered power is then 




{El HI* - El 

( 21 ) 

where Ee denotes ‘^‘Real part of . . and the integral 
is extended over the surface of a large sphere of radius 
r. In our case, using equations (16) and (17), one 
gets 

^ ■ ■ {\El\^+\El\^) r 

( 22 ) 

In the case of an absorbing sphere, the net flow of 
energy across a closed surface around the sphere is 
absorbed energy flow, and it is directed inward. One 
may thus write that this absorbed energy, which dis- 
appears in the form of heat, is 




n 


sm 


Pab = Re 




Sc) sin dddd<t>. (23) 


Since the integral of the incident flow across a closed 
surface is zero, equation (23) in connection with 
equation (21) leads to the definition of the rate of 
flow of total energy or the power subtracted from 
the beam, i.e., (Pab + Ps)} as an integral over a closed 
surface of the third term on the right-hand side of the 
radial component Sc ot the Poynting vector, equation 
(19). Thus 

P. = Pci + p. = h (- Re) 


sm 


(24) 

Substituting equations (16) and (17) into equation 
(24) and remembering that the cf> integration leads 


to a factor tt and that the integrals over products of 
the associated Legendre polynomials P\{x) are dif- 
ferent from zero only in the following combination of 
these products appearing in equations (22) and (24), 




sin Odd = 


one finds. 


2 

2a 2- -f- 1 

[n{n-\- 1)]2 , 


and 


P. = 


2 ^ 

^ 2 (2»+l)(|a:i2 + 16).12), (25) 


P< = ^ (- Re) 2 (2» + 1) « + 60 . (26) 

We shall also need the fraction of the power scat- 
tered backwards by the sphere, i.e., in the direction 
6 = TT, per unit solid angle. One thus obtains, with 
do) = sin 9d6dcl>, 




CO CO 

Re 2 2(-) 

n= 1 m= 1 


n+m 

(2«+l)- 


(2m+l)«-6D(o:*-b;*), (27) 


as a simple calculation shows, starting from equation 

( 22 ). 

It has already been mentioned in connection with 
the definition of the complex wave number, equation 
(2), of a homogeneous and isotropic medium that its 
imaginary part is chosen to be negative. We shall 
write 

jk = a i/3, (28) 

where ^ is the phase constant and a the attenuation 
constant; both are real. The explicit expressions of /3 
and a in terms of the characteristic electromagnetic 
properties of the medium, namely, inductive capacity 
e, permeability ju, and conductivity o- for the given 
frequency <o/27r are the following 



With equation (28) the field strength, electric or 
magnetic, in a plane wave propagated in such a 
medium along, say, the z axis, is, omitting the time 
factor, of the form: 

F = Fo 

Fo being an amplitude vector directed along either one 
of the two remaining coordinate axes. The attenuation 


154 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


factor a simply means that in this medium an advance 
of the wave through a distance of 1/a meter is accom- 
panied by a decrease in the field strengths in the ratio 
of 1 = 0.368, or the power per unit area (Poynting 

vector) decreases in the same ratio over half that dis- 
tance or 1/2 a meter. 

In the mks system, the attenuation factor is then a 
nepers per meter, whereas the power absorption co- 
efficient is 20a (logio^) decibels per meter = 8.686a 
db per meter. 

Our problem is the study of propagation in a medi- 
um which is neither homogeneous nor isotropic, inas- 
much as it consists of a suspension of water droplets 
in the atmosphere. It can be proved that in such a 
medium the attenuation factor is the sum of all the 
different partial attenuation factors due to different 
physical phenomena. 

The particle attenuation factor will still be denoted 
by a. More appropriately we might call a the average 
particle attenuation factor. It may be defined as 

a =-NQt neper per unit length, (31) 

where N is the average number of water drops per 
unit volume and Qt the total cross section of one 
droplet. The absorption effect of one spherical water 
drop is given by Qt which is the ratio of the power Ft 
removed by the drop from the beam falling on it to 
the incident power per unit area. Provided the effect 
of all the drops be linearly additive, equation (31) 
will express their average attenuation effect. The 
incident power density is the complex Poynting vector 
of the beam 

S.M = ^ ■ (32) 

Therefore, with equations (3) and (26), 

00 

0, = ^ (-Re) X (2n+l) « + K), (33)o 

where X = 27^/^^2 is the wavelength of the radiation 
in air or free space. Similarly the cross section for 
scattering is, with equation (25), 

00 

0.= ;^- X(2« + 1)(I<|^ + |61P). (34) 

The differential cross section for back scattering (or 

‘‘The minus sign is missing in the presentation in reference 
18a; see formulas (26) and (29) on page 569. This leads to the 
incorrect result, for nonabsorbing spheres, that the scattering 
cross section Q» reduces in this case to the negative of the 
total cross section Qt. Clearly Qg reduces to +Qt. 


radar cross section) is then, with equations (27) and 
(32), 

z c-r(2.,+i)- 

(2m+l) [ay„*+b:b:,*-2aX*]. (35) 

These are the formulas on which the computations of 
attenuation have been based. They are certainly cor- 
rect in the wavelength region 1 cm to 100 cm with 
which the present study is mainly concerned, and they 
correctly take into account the linear dimensions of 
the scattering and absorbing particles. According to 
Brillouin^® these formulas have to be modified in the 
limit \<^ a, in which case for i^erfect reflection they 
lead to a scattering cross section 27ra^, double of the 
expected geometrical cross section. Since the modifica- 
tions mentioned do not play any role for X > 3a/ 10, 
which condition will always be satisfied in the present 
report, they will not be discussed here. 

10.1.3 Scattering Amplitudes® 

< and hn 

The scattered fields (E^, H^) outside the sphere 
and the transmitted fields (E<, H<) inside are due to 
forced oscillations of the sphere caused by the in- 
cident field (Ei, Hi). The fields (E^, and (E^, 
Hi ) given by equations (7) and (8) can be regarded 
as due to electric and magnetic 2”-poles (a = 1 cor- 
responds to dipoles, n = 2 to quadrupoles, etc.) in- 
duced in the substance of the spherical particle. In 
the steady ^tate these poles oscillate with the fre- 
quency of the incident radiation field. When this fre- 
quency approaches a characteristic frequency of the 
free vibrations of the electric or magnetic 2”-poles of 
the sphere, resonance will occur. It can, indeed, be 
shown that the amplitudes are associated with 
vibrations of magnetic poles and the hnS with vibra- 
tions of electric poles. The characteristic frequencies 
of the free vibrations of magnetic poles of a sphere 
are determined by a condition which annuls the de- 
nominator of an, those of electric poles by a condition 
which annuls the denominator of hn, given by equation 
( 14 ) 18 b qqjg characteristic frequencies of the free 
vibrations are, however, complex in contrast with the 

®Since henceforth we will deal only with the scattering co- 
efficients a®, 6;k we will omit the superscript s. 


ATMOSPHERIC ABSORPTION AND SCATTERING 


155 


real frequency of constraint of the radiation field 
falling on a sphere, as in the present case. The de- 
nominators of the amplitudes a„ and tn, although re- 
duced, can never become zero, and there are no diffi- 
culties caused by resonance. 

A glance at the formulas (14) shows the com- 
plexity of the amplitudes a,, and An exact com- 
putation of these coefficients is out of the question on 
account of the lack of tables of Bessel and Hankel 
functions of complex argument in the range needed 
here. They reduce to simple expressions in the limit 
when the parameter p = 27ra/A^ 1. In the present 
work we shall be mostly interested in the cases where 
p < 1 or p 1. In these cases a series expansion of 
the amplitudes in ascending powers of the parameter 
p can be used. With the expansions of the spherical 
Bessel and Hankel functions 


(i) 


(p) 


. (3) 


(p) 


2„ „ y (-)"(» + ”»)! 

„ = o™n2» + 2TO+ 1)! 

y (-)"(» + ”»)! 

»»!(2w + 2to+ 1)! 


1 


P 


2m 


I 3 y (2n - 2 to)! 

2^ ^ n ^ - ( ^ )• 

used in equation (14), one is lead to the following 
amplitudes, keeping the first few terms of the ex- 
pansions and assuming = ^ 2 ? i-®*? the equality of 
the permeabilities of the medium and the sphere: 


a„ = - ^ 


i) 


(2»+l)!/ 2«+3 

JV2 - 1 


^2„+3. 


2n + 1 
6 


2(2ra + 


y-4 


(36) 




(2w + 1) (w+ 1) (iV^- 1) 
nN‘‘‘ + n + 1 


2is+l . 


(37) 


j , , (2n+l)[(2n-l) iV^-n-1] 

(2» + 3) (2w- 1) (niV^H- n+ 1) 


\(2»+l)!/ 


( 2 »+ 1 )! 

(2n + 1) (n + 1) — 1) 2 n+i 


+ 




From these expressions one derives at once the ex- 
plicit formulas representing the induced magnetic 
dipole (^i), electric dipole (&i), and electric quad- 
rupole (h.,) amplitudes. One has, then, neglecting 
powers of p higher than the sixth, 

ai=^(/V^- 1)P•^ 

45 ' 

/ 3^ 

3^2 + 2 \ 5W2H-2 


and 



iV2- 1 

iV2 + 2 



(38)' 




15 2iV2 + 3 


It would appear interesting to present the relation- 
ships connecting the amplitudes of the electric and 
magnetic poles an and hn with those appearing in the 
treatment of Mie which was used by Ryde.^^ The 
magnetic and electric amplitudes in Mie’s notation 
are respectively pn and a„, and the relationships in 
question are the following: 


p„Mie = (—)nj (2n + 1) an, 

{-)n+lj(2n+l)bn. (39) 

Finally the formulas (38) can be transformed so 
as to have the real and imaginary parts of the ampli- 
tudes separated easily. The refractive index N of the 
spheres is connected with their complex dielectric 
constant by 

ec= = €r — j€i, (40) 

or with 

N = n(l- jx), (41) 

the complex index of refraction, one has 

= n2 (l-x");€, = 2^2^. (42) 


^Some misprints and slight errors in the expressions for 
these amplitudes may be noted in reference 18a. On page 571 
in the formula (35) and in the denominator of the coefficient 
of p2, read (2n + 2) instead of (2n + 1 ). In the formula (36) 
the minus sign on the right-hand side is missing. In reference 
18a, 6 r and 62 have the wrong sign and the term in bi^ 
is incomplete. It is recalled that +i has been replaced through- 
out this report by —j. 


nN^ + n + 1 


156 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


Using equation (40) in the amplitudes (38) one 
gets 

^ i (€r — 1) ] p®, 

45 

- 2€i , 2 


(€r + 2)^ + €i^ 5 

[(e. + 2) (7er- 10) + 76,^] ^ _ 4 
[U, + 2)2 + €.-^]2 " 9 

(6, - 1) + 2) ^ [ 2 (e, - 1) (f, + 2) - 9] + s 

[(€. + 2)>> + «i2]>> 

2fe-2)(^H:2^^ 2. 

3 (er + 2)2 + *^2 5 

(« - 1) (6-2) (t.+2)2+e.-2[2(t,+ l)2- (3t,4-20)]+e.-‘ 
[(e. + 2)2 + €fl^ 

5 , 1) (t. + 2) + , 

'’ 3 [(€,+ 2)2 + «,2]2 


J ^ 1 - (i/5) [(e.- 1) (26, + 3) + 2e,2] 

' 3 (2e, + 3)2 + 4e<2 

(43) 

These amplitudes are the same as those found by 
Ryde.^ They allow the computation of attenuation 
and back scattering with a certain approximation. 
The results thus obtained are the more accurate, the 
smaller the parameter p = 27ra/\. 

In the computation of the amplitudes a„ and 
we have used the same values of the real and imag- 
inary parts of the dielectric constant of water €r and 
a as the ones used by Ryde. These were obtained by 
using the Clarendon Laboratory values for cr and ci 
for waves of 1.26-cm wavelength^^ and determining 
with them the transition wavelength Aq in the Debye^® 
formulas 


> '•■ = T (44) 

'Mr) ‘ 

€ o^p = 1.33, €00 = 81, Xo= 1.59 cm. 

The values of cr computed with these formulas happen 
to be in fair agreement with the experimental values 
obtained by a large group of independent workers.^^’^“ 
There seems to be a regrettable situation concerning 
the values of ei, and no serious studies have been made 

‘'In his first report Rydei"^ gave incorrectly the coefficients 
of in both the real and imaginary parts of 61 . The coefficient 
of in the real part was corrected in the second report. In 
comparing the 6 i’s with the amplitudes given by Ryde, the 
relations (38) have to be taken into account. 


Table 1. Values of the dielectric constant of water at 
t ^ 18 C, used in this work.* 


X, cm 

€r 

€i = 60o-X 

<r mhos/m 

1 

24.2 

35.6 

5.93 X 10 

1.26 

32.5 

38.6 

5.11 X 10 

1.62 

43.3 

39.5 

4.13 X 10 

2 

50.6 

38.5 

3.20 X 10 

2.5 

58.2 

35.9 

2.39 X 10 

3.0 

63.6 

32.7 

1.81 X 10 

4.0 

70.3 

27.2 

1.13 X 10 

5 

73.8 

22.7 

7.56 

6 

76.0 

19.3 

5.36 

8 

78.0 

15.1 

3.15 

10 

79.0 

12.3 

2.05 

15 

81 

8.40 

9.33 X 10-1 

20 

81 

6.30 

5.25 X 10-1 

30 

81 

4.20 

2.33 X 10-1 

50 

81 

2.52 

8.40 X 10-2 

75 

81 

1.68 

3.73 X 10-2 

100 

81 

1.26 

2.10 X 10-2 


*The computations of the attenuation and scattering effects are all 
based on this table and refer therefore always to temperatmes of about 
18 C, unless stated otherwise. 


Table 2 . Temperature variation of the dielectric 
constant of water (K band). 


Degrees C 

€r 


Water 3 

27 

27 

25 

35 

23 

60 

44 

14 

Ice — 15 

3.3 

0.011 


on the temperature and frequency variation of this 
quantity, so fundamental for the microwave region. 
A beginning in this direction has been undertaken by 
the Radiation Laboratory.^-"^ In Figure 4 we have 
drawn the curves €r(A) and ci(A) in the range 1 to 11 
cm, and Table 1 gives the values of the dielectric con- 
stant used in this work in the wavelength interval 1 
to 100 cm. 

It is interesting to consider here the temperature 
variation of cc- Recent measurements made in the 



Figure 4. Dielectric constant of water (<>^18 C) cc = 
fr—Jeu 


ATMOSPHERIC ABSORPTION AND SCATTERING 


157 


Radiation Laboratory in the K band^^ gave the results 
shown in Table 2. 

As might have been expected, the dielectric absorp- 
tion ci increases with decreasing temperature. 

With the above values of cr and ci the computation 
of the amplitudes an and hn is straightforward. The 
amplitudes and hn have the form 
00 

(45) 

l=2n+3 

b„= i (46) 

Z= 2/1+1 

Thus we let denote the real part of the coeffi- 
cient of p® in and its imaginary part. Similarly, 
are the real and imaginary parts of the co- 
efficient of in etc. 

As equation (43) shows andai^®^ are directly 
proportional tO‘( — c{) and (er — 1) respectively. As 
the wavelength increases, changes approximately 
from — 0.9 to — 0.03 after passing through a shallow 
minimum on account of the variation of €{. In the 
same interval increases from about 0.5 to 1.8. 

turns out to be practically negligible, in com- 
parison with which is almost constant in this 

wavelength range. and behave similarly. 

With and the roles are inverted. 

Finally ^2^®^ and both vary in the range under 
consideration. 

As a rule, those coefficients of the powers of p ( = 
ttD/X) {D = diameter of the spliere) which do not 
contain terms in and powers of cr separately in the 
numerator, but only the products cr €i, and powers 
of c{, are considerably smaller than those which do 
contain er and its powers separately. 

10.1.4 Attenuation of Radio Waves 

by Spherical Raindrops 

The knowledge of the coefficients and hn allows 
finally the computation of the absorption cross section 
for any spherical water drops of given diameter D at 
those temperatures where the amplitudes can be 
computed. 

The absorption coefficient becomes, with the cross 
section found above, [equations (33) and (43)], 

**The attenuation values given in this report refer always 
to one-way transmission and are additive to the free space 
attenuation. 


a = 0.4343 X W ~ (- Re) 2. (2n+ 1) (un + bn) 

n = l 

db per kilometer. (47) 

In our approximation /for the amplitudes, we may 
write 

SirNV 

a = 0.4343 X W (ci + + c^p^ + . . .) 

A 

db per kilometer (48) 

where N is the number of spherical drops, each of 
volume V per cubic centimeter, A is the wavelength in 
centimeters of the incident radiation. The parameter 
p is, as above, irD/X, D being the diameter in centi- 
meters of a drop, and the coefficients Cj, C2, C3, • • • are 
the following functions of the wavelength, the tem- 
perature of the drops being taken as a constant (/<-' 
18 C), 

_ Oe; 


_ , 5 

" 15 3 (2er+3r+W 

6 6,[(€.+2)(76.-10)+7e/] 

5 [(e,+2)2+e,2]2 

^ ^ 4 (6.-l)^(6.+2)^+€.-^[2(e.-l)(6.+2)-9]+6,-^ 

3 [(g^-j_2)2-pg^.2] 

It is possible to give the attenuation formula another 
simple form by noticing that NV is the total volume 
of water per eid)ic centimeter in tlie form of drops or 
10*’ NT' is the total volume of water per cubic meter. 
Since the density of water is 1 g per cubic centimeter, 
numerically, the quantity 10*’ NV is the mass m of 
liquid water per cubic meter, in air. The transformed 
attenuation formula becomes finally 


a = 4.092 — (ci + C2p2 + C 3 p^+ • • •) db per kilometer. 

^ (50) 

It is seen that when p = ttD/X « 1 so that all the 
terms in the expansion in equation (50) are small in 
comparison with Cj, the attenuation factor reduces to 


4.092 mci 24.55 mei 
“ X - X (€,+2)2+6^ 

db per kilometer. (51) 

Hence, when the diameter of the water drops is very 
small in comparison with the wavelength of the inci- 
dent radiation, the attenuation does not depend on the 


158 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


size of the drops but only on the total mass of liquid 
water per unit volume contained in the air. It is in- 
teresting to find, for a given wavelength, the largest 
diameter for which the approximation (51) can still 
be used in practice. If it is practical to use (51), (as 
in reference 12), for 

< ^ . (52) 

then in order that (51) shall represent the attenuation 
factor within 10 per cent, the diameter of the spheres 
must (for given A), be equal to or less than Dc with 

- fo ©’ 

In Table 8 appear the values of Co, and Dc in the 
wavelength range 1 to 100 cm. The values of are 
not included, since this coefficient turns out to be 
practically constant, in this range, increasing from the 
value of 1.224 for A = 1 cm to 1.239 for A = 100 cm. 

It is evident that for values of p which are not too 
small, equation (48) or (50) has to be used. When 
p is sufficiently close to unity these series cease to give 


Table 3 


A, cm 

Cl 

C2 

Dc cm 

1 

0.109 

2.53 

0.0656 

1.1 

0.0994 

2.60 

0.0680 

1.26 

0.0862 

2.69 

0.0713 

1.5 

0.0730 

2.73 

0.0774 

2 

0.0543 

2.64 

0.0906 

3 

0.0365 

2.23 

0.121 

4 

0.0273 

1.85 

0.154 

5 

0.0217 

1.54 

0.187 

6 

0.0179 

1.31 

0.222 

8 

0.0137 

1.01 

0.293 

10 

0.0110 

0.835 

0.363 

15 

0.00724 

0.570 

0.534 

20 

0.00541 

0.427 

0.712 

25 

0.00437 

0.342 

0.892 

30 

0.00364 

0.285 

1.07 

50 

0.00219 

0.171 

1.78 

75 

0.00146 

0.114 

2.68 

100 

0.00109 

0.085 

3.57 


any good values of the absorption cross section Qt or 
the attenuation factor a. In the K and X bands, Eyde 
and Hyde^^ have, therefore, computed the attenuation 
factors exactly. These computations were included 
(without being checked) in Tables 4 and 5, where Qt 
and a have been computed for a series of drops ranging 


Table 4. Absorption cross section Qt (cm2) of water drops with diameter D (cm). 


\ 

X.cm^ 

0.05 

0.10 

0.15 

0.20 

0.25 

D, cm 

0.30 

0.35 

0.40 

0.45 

0.50 

0.55 

1.25 

6.19 10-5 

9.60 10-4 

5.66 10-3 

1.89 10-2 

5.04 10-2 

1.13 10-1 

2.1510-1 

3.66 10-1 

5.66 10-1 

7.62 10-1 

1.01 

3 

9.19 10-6 

1.52 10-4 

1.30 10-3 

5.53 10-3 

1.63 10-2 

3.73 10-2 

6.65 10-2 

1.08 10-1 

1.52 10-1 

2.1510-1 

2.72 10-1 

5 

2.84 10-6 

2.75 10-5 

1.20 10-4 

3.79 10-4 

9.85 10-4 

2.24 10-3 

4.59 10-3 

8.68 10-3 

1.54 10-2 

2.59 10-2 

4.18 10-2 

8 

1.09 10-6 

9.49 10-6 

3.65 10-5 

1.02 10-4 

2.40 10-4 

4.98 10-4 

9.63 10-4 

1.74 10-3 

2.97 10-3 

4.85 10-3 

7.63 10-3 

10 

6.90 10-7 

5.84 10-6 

2.1610-5 

5.76 10-5 

1.46 10-4 

2.59 10-4 

4.81 10-4 

8.44 10-4 

1.40 10-3 

2.25 10-3 

3.47 10-3 

15 

2.98 10-7 

2.45 10-6 

8.66 10-6 

2.1810-5 

4.59 10-5 

8.65 10-5 

1.51 10-4 

2.51 10-4 

3.98 10-4 

6.10 10-4 

9.06 10-4 

20 

1.67 10-7 

1.36 10-6 

4.71 10-6 

1.15 10-5 

2.36 10-5 

4.31 10-5 

7.29 10-5 

1.17 10-4 

1.78 10-4 

2.66 10-4 

3.85 10-4 

30 

7.36 10-8 

5.93 10-7 

2.02 10-6 

4.88 10-6 

9.74 10-6 

1.73 10-5 

2.83 10-5 

4.38 10-5 

6.48 10-5 

9.29 10-5 

1.30 10-4 

50 

2.67 10-8 

2.14 10-7 

7.27 10-7 

1.73 10-6 

3.41 10-6 

5.96 10-6 

9.57 10-6 

1.45 10-5 

2.09 10-5 

2.93 10-5 

3.97 10-5 

75 

1.19 10-8 

9.44 10-8 

3.21 10-7 

7.63 10-7 

1.49 10-6 

2.60 10-6 

4.1510-6 

6.23 10-6 

8.94 10-6 

1.24 10-5 

1.66 10-5 

100 

6.77 10-9 

5.41 10-8 

1.83 10-7 

4.34 10-7 

8.50 10-7 

1.47 10-6 

2.35 10-6 

3.51 10-6 

5.02 10-6 

6.92 10-6 

9.27 10-6 


Table 5. Attenuation a/N (db/km) in fictitious rains with a concentration of one drop per cubic centimeter of D cm 


diameter. 


X, cm'X 

0.05 

0.10 

0.15 

0.20 

D 

0.25 

, cm 

0.30 

0.35 

0.40 

0.45 

0.50 

0.55 

1.25 

2.69 10 

4.17 102 

2.46 103 

8.23 103 

2.19 104 

4.90 104 

9.33 104 

1.59 105 

2.46 105 

3.31 105 

4.37 105 

3 

3.99 

6.61 10 

5.63 102 

2.40 103 

7.08 103 

1.62 104 

2.89 104 

4.68 104 

6.61 104 

9.33 104 

1.18105 

5 

1.23 

1.19 10 

5.22 10 

1.65 102 

4.28 102 

9.72 102 

1.99 103 

3.77 103 

6.69 103 

1.13 104 

1.81 104 

8 

4.73 10-1 

4.12 

1.59 10 

4.43 10 

1.04 102 

2.16102 

4.18102 

7.54 102 

1.29 103 

2.10 103 

3.31 103 

10 

2.99 10-1 

2.54 

9.37 

2.5 10 

6.35 10 

1.12102 

2.09 102 

3.66 102 

6.09 102 

9.76 102 

1.51 103 

15 

1.30 10-1 

1.07 

3.76 

9.47 

1.93 10 

3.76 10 

6.58 10 

1.09 102 

1.73 102 

2.65 102 

3.93 102 

20 

7.26 10-2 

5.89 10-1 

2.04 

5.02 

1.03 10 

1.87 10 

3.1710 

5.07 10 

7.73 10 

1.15 102 

1.67 102 

30 

3.20 10-2 

2.57 10-1 

8.7910-1 

2.12 

4.23 

7.50 

1.23 10 

1.90 10 

2.82 10 

4.04 10 

5.63 10 

50 

1.1610-2 

9.29 10-2 

3.16 10-1 

7.53 10-1 

1.48 

2.59 

4.16 

6.29 

9.10 

1.27 10 

1.72 10 

75 

5.1610-3 

4.1210-2 

1.39 10-1 

3.31 10-1 

6.49 10-1 

1.13 

1.80 

2.70 

3.88 

5.37 

7.21 

100 

2.94 10-3 

2.35 10-2 

7.93 10-2 

1.89 10-1 

3.69 10-1 

6.40 10-1 

1.02 

1.53 

2.18 

3.01 

4.03 


ATMOSPHERIC ABSORPTION AND SCATTERING 


159 


in diameter from 0.05 to 0.55 cm. For wavelengths 
X > 5 cm, the three-term series expansion (48) was 
used. It is expected that at these shorter waves, where 
the critical diameters are smaller than the drop diam- 
eters mentioned, the cross sections and attenuation 
factors given in the tables will be but fair approxima- 
tions of the exact values of these quantities. 

The range of values of p covered by these tables ex- 
tends from about p = 0.0016 to p = 1.4. In Figures 
5 and 6 two families of curves are drawn giving 
Qt (A)/) and (x(X)j)/N, the diameter of the drops being 
kept constant, and Qt{D)^ and a(Zl)^/iV, the wave- 
length of the radiation being kept constant. Since our 
computations cover the range from A = 5 cm, we have 
extended our curves on Figure 5 so as to cover the K 
and X bands, using the values of the cross sections and 
attenuations given in these bands by Ryde and Ryde. 
Their data are represented again in the upper curves 
of Figure 6. 

We are now prepared to apply these results to 
meteorological phenomena and shall, for this purpose, 
give a summary of typical data on clouds, fogs, and 
rains to be used in this work. 

10.1.5 Typical Data on Clouds, Fogs, 
and Rains 

To compute the attenuation due to the different 
forms of condensation demands a knowledge of the 



Figure 5. Absorption cross section, Qt, and attenua- 
tion constant, a, of spherical water drops as a function 
of the wavelength. The abscissa gives the wavelength, 
X, in centimeters. The right-hand ordinate scale gives 
logio {ot/N), where a/N, the attenuation constant in a 
rain with 1 drop per cu cm, is expressed in decibels per 
kilometer. The numbers on the curves give the diameter, 
D, of the drops in centimeters. The left-hand ordinate 
scale gives logio Qt with Qt being expressed in square 
centimeters. 



D IN CM 


Figure 6. Absorption cross section, Qt, and attenuation 
constant, a, of spherical water drops as a function of the 
drop diameter. The abscissa gives the drop diameter, 

D, in centimeters. The right-hand ordinate scale gives 
logio (oc/N), where a/N, the attenuation constant in a 
rain with 1 drop per cu cm, is expressed in decibels per 
kilometer. The numbers on the curves give the wave- 
length, X, of the incident radiation in centimeters. The 
left-hand ordinate scale gives logio Qt, with Qt being 
expressed in square centimeters. 

water drop size distributions and their volume concen- 
tration. Indeed, if such a form of condensation con- 
tains Njc droplets per cubic centimeter having a diam- 
eter of k cm, with k varying from, say, 0 to s, then the 
attenuation factor due to this form will be the sum 
of the attenuation factors associated with each of the 
different drop groups with diameter of 1, 2, , 

. . . , n, . . • , 5 cm. In other words, 

s s 

«totai = ^ otk= 0.4343 X 10® 2 ^kQt,k 

k=0 k=0, 

db per kilometer, (54) 

according to equation (31), where Njc is the number 
per cubic centimeter of the drops k, and Qt,k is the 
total absorption cross section in square centimeters 
of one spherical water drop of diameter k cm. 

It was shown above that theory allows a precise com- 
putation of the cross sections Qt, provided the dielec- 
tric constant of water is given at the temperature of 
the drops. The concentration of is a purely meteor- 
ological datum and must be obtained experimentally. 
As far as as the writer is aware, data on drop concentra- 
tions and drop size distributions are extremely scarce, 
and it appears that no systematic researches have as yet 
been undertaken for the purpose of obtaining such data. 


160 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


Recently, observations were made available on drop 
size distributions in clouds of different types.®’® The 
main results of interest to the attenuation problem are 
that in clouds of different altitudes the diameter of 
the drops does not seem to exceed 0.02 cm. The liquid 
water content of the clouds examined by Mazur® varied 
between about 0.15 and 0.50 g/m®. The results of 
Diem® are, on the whole, similar. 

Some data on ice clouds are included in Best’s 
memoranda. 

Data on fogs are extremely meager. The diameter of 
fog droplets appears to be of the same order of mag- 
nitude as those of liquid water clouds.®^’^^ Humphreys, 
in his table of precipitation values, gives 0.006 g/m® 
as the liquid water content in fog. 

The data on rains used in this report are those from 
reference 11. For additional data recently collected 
see reference 26. 

The most important set of data which is directly 
usable in this work is contained in Table 6. In the 
last row of this table p is the precipitation rate or rate 
of rainfall, expressed in millimeters per hour, and 
results directly from the total volume of water fall- 
ing per square meter per second, since p = 36 X 
10"^ F, where V is expressed in cubic millimeters per 
square meter per second. 

Rains 1 and 2 refer, according to Best,^^ to a rain 
looking very ordinary, falling over a large area. Type 
3 is a rain with breaks and sunshine. Type 4 corre- 
sponds to the beginning of a short rainfall like a 
thundershower. Type 5 refers to a sudden rain from 
a small cloud, associated with a calm, sultry atmos- 
phere. Type 6 was a violent rain like a cloudburst with 


some hail. Types 7, 8, an 9 are for the heaviest period 
and the period of stopping of a continuous fall which 
at times took the form of a cloudburst. The preceding 
characteristics of the rains in Table 6 are quotations 
from the paper of Best. 

These data on drop size distributions are the only 
data available to the writer. Clearly the rate of rain- 
fall cannot be correlated from these data to any drop 
size distribution. A priori, it seems unlikely that a 
strict correlation between drop size distribution and 
rate of rainfall should exist. To a rain of given drop 
size distribution corresponds necessarily a determined 
rate of rainfall, but the reverse is not true, since a 
given rate of rainfall might be obtained with a large 
variety of drop size distribution.^® In other words, 
the drop size distribution is the only physical charac- 
teristic of a rain as far as attenuation and back scat- 
tering (echo) of radiowaves are concerned. 

In any one location, even the drop size distribution 
of a rain is but an instantaneous characteristic of that 
rain. No data are available concerning the fluctuations 
in time of drop size distribution. 

The space distribution of raindrops is another prob- 
lem on which too few data are available. According 
to Kerr and Rado,^® K-band rain absorption experi- 
ments over a relatively short path ( -^4km) have shown 
that the simultaneous rates of rainfall at three points 
of such a path were almost invariably appreciably 
different. The rates were measured at the location of 
the transmitter, the receiver, and at a point in be- 
tween. Needless to say, under such circumstances the 
possibility of a quantitative interpretation of the ex- 
perimental data on attenuation is almost excluded. 


Table 6. Drop size distributions in rains. 


Number of drops/m^/sec in nine different types of rain 


D, cm 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.05 

1,000 

1,600 

129 

60 


100 

514 

679 

7 

0.10 

200 

120 

100 

280 

50 

1,300 

423 

524 

233 

0.15 

140 

60 

73 

160 

50 

500 

359 

347 

113 

0.20 

140 

200 

100 

20 

150 

200 

138 

295 

46 

0.25 



29 

20 

0 

0 

156 

205 

7 

0.30 



57 


200 

0 

138 

81 

0 

0.35 





0 

0 

0 

28 

32 

0.40 





50 

0 

0 

20 

39 

0.45 






200 

101 


0 

0.50 





- . . 

. . . 



25 

Total No. 

of drops 

1,480 

1,980 

488 

540 

500 

2,300 

1,840 

2,180 

500 

Total 

volume 

mm3/m2/sec 1,005 

1,112 

1,656 

681.2 

5,258 

11,970 

9,535 

6,298 

4,236 

p mm /hr 

3.6 

4.0 

6.0 

2.46 

18.9 

43.1 

34.3 

22.6 

15.2 


ATMOSPHERIC ABSORPTION AND SCATTERING 


161 


It may be meiitioiied here that the earlier attenuation 
experiments on 1-cm waves by Robertson and his col- 
laborators^^ as well as those of Mueller^ on K/2 band 
were made over a shorter path (about 400 meters) 
and the rate of rainfall was measured only at one 
place, roughly in the middle of the path. Since the 
path length of the Oxford workers^® was 2 km, there 
was ample room for possible fluctuations in the rate 
of precipitation. The K-band radar transmission 
studies by the Bell Telephone Laboratory workers 
were made over longer paths,^® and here, too, a situa- 
tion somewhat similar to those reported by the Radia- 
tion Laboratory workers might have existed, as the 
authors duly noticed it. 

The meteorological irregularities which thus seem 
to be inherent in precipitation data eliminate the pos- 
sibility of a quantitative theory of attenuation and 
back scattering of radiowaves by rains or other pre- 
cipitation forms. Although the data contained in 
Table 7 are used extensively in this report, the re- 
sults thus obtained should be regarded as semiquan- 
titative indications rather than rigorous theoretical 
predictions. 

Given the number of raindrops of known dimen- 
sions falling over a certain area in a given time and 
given also the terminal velocity of the drops, the 
spatial concentration of raindrops can be derived at 
once. In Figure 7 the terminal velocity curve is drawn 



Figure 7. Terminal velocity of raindrops (experi- 
mental). 


as a function of drop diameter. These velocities were 
measured at Porton and are quoted in BesPs paper.^^ 
From Table 6 we may obtain data for Table 7, 
giving raindrop concentration of drops with diam- 
eter h=D cm. These concentrations, as are the data in- 
cluded in Table 6, may be regarded as characteristic 
for rains of the indicated precipitation rate, but they 


are not necessarily typical for those rains. Also given 
is the liquid water content of the atmosphere as- 
sociated with the rains of Table 6 and its graphical 
representation in Figure 8. The curve drawn on this 
graph should not, however, be considered as represent- 
ing any functional relationship between the liquid 



Figure 8. Computed liquid water distribution (cm^/ 
m3 or g/m3) based on experimental drop size distribu- 
tions in different rains. The slope of the straight line 
approximation is 0.038 g/m^/mm/hr. 

water concentration of the rainy atmosphere and the 
rate of rainfall. It can indeed easily be proved that 
the liquid water concentration associated with a rain 
depends only on the fractional precipitation rates of 
the different drop groups. It does not depend directly 
on the total rate of rainfall. Any rain of given total 
precipitation rate can be built up by a number of drop 
size distributions which determine different liquid 
water concentrations in the atmosphere. This means 
that it is theoretically incorrect to draw a graph entitled 
‘‘^Liquid Water Concentration versus Rate of Rainfalfl^, 
as is frequently done. A curve so drawn can however be 
of considerable practical value when rough concentra- 
tions corresponding to given rates of rainfall are 
desired. 

It can be seen that the resulting liquid water dis- 
tributions are in fair agreement with those reported 
by Humphreys in his table of precipitation values^® 
already mentioned. It may be added here that aloft 
and in certain parts of rain clouds, where considerable 
updraft exists, the drop concentrations may be ex- 
pected to be larger than those derived from Table 6. 

These data will now be used in the computation of 
attenuation and back scattering by the different pre- 
cipitation forms, assuming always ideal conditions 
and leaving aside the above-mentioned irregularities 


162 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


Table 7. Number of raindrops per cubic meter in rains of different precipitation rates. 


Distribution 



A 

B 

C 

D 

E 

F 

G 

H 

I 

D, cm 

2.46 

3.6 

4.0 

6.0 

p, mm/hr 
15.2 

18.7 

22.6 

34.3 

43.1 

0.05 

28.5 

476 

752 

61.4 

3.33 


323 

245 

47.6 

0.10 

71.8 

512 

30.8 

25.6 

59.7 

12.8 

134 

108 

333 

0.15 

31 

27 

11.4 

14 

21.5 

9.52 

66 

68.4 

95.2 

0.20 

3.13 

22 

31.2 

15.6 

7.2 

23.4 

46.1 

21.6 

31.2 

0.25 

2.76 


. . . 

4.0 

0.96 

0 

28.3 

21.5 

0 

0.30 




7.2 

0 

25.3 

10.2 

17.6 

0 

0.35 




• • . 

3.83 

0 

3.35 

0 

0 

0.40 



. . . 


4.48 

5.75 

2.3 

0 

0 

0.45 



... 

... 

0 


... 

11.3 

22.5 

0.50 

... 


... 


2.71 




^ 

Liquid water 

g/m^ 0.130 

0.439 

0.217 

0.242 

0.521 

0.673 

0.930 

1.25 

1.55 


ill space. For reasons stated above, theoretical results 
are significant only with regard to orders of magnitude. 

10.1.6 Attenuation by Idealized 

Precipitation Forms 

The data included in the preceding section show, 
first of all, that in clouds and fogs the attenuation 
can be given rigorously. Indeed, Table 3 indicates 
that the critical diameter even for waves of 1-cm 
wavelength is over 0.06 cm. Since we have seen that 
in clouds and fogs the drop diameters never exceed 
0.02 cm, it appears that formula (51) is applicable, 
and the attenuation of all waves of wavelength A > 
1 cm is independent of the size of the drops. Further- 
more, taking m = 1 g per cubic meter in formula 
(51) one probably obtains an upper limit for the 
attenuation of these waves.* In Figure 9 the atten- 
uation is plotted down to A = 0.2 cm. The dielectric 
constant of water has been computed in this range by 
using the Debye formula for wavelengths A > 1 cm. 
Clearly the attenuation in fogs and clouds even in 
the region A 1 cm is not of great importance ex- 
cept for long ranges and radar observations. The 
attenuation becomes negligible for waves with A > 
10 cm. 

Table 3 also shows that the attenuation becomes 
practically independent of the drop size distribution 
for wavelengths equal to or larger than about 20 cm. 
In the 5- to 20-cm range the three-term formula 

•Attention may be called to the absence of data on the 
liquid water distributions in heavy sea fogs. 


(48) or (50) in connection with (54) will represent 
fairly well the attenuation in different rains, with 
increased accuracy at longer Avavelengths. Below A 
= 5 cm this formula is inapplicable, but there Ryde 



0.004 » ■ ..1 ■ ■ I : 3 

0.2 0.5 1.0 2 5 10 

A IN CM 

Figure 9. Attenuation factor in liquid clouds and fogs. 


t=lS C. 


ATMOSPHERIC ABSORPTION AND SCATTERING 


163 


and Kyde’s^^ exact attenuation values are available. 
The attenuation formula in a rain, as given by equa- 
tion (54), can be transformed easily to another form. 
If Pic denotes the partial precipitation rate of the drops 
of k cm diameter in a given rain of total precipitation 
rate p, then clearly, 

•S 

p=^Vk, (55) 

s being the diameter of the largest drops in this rain. 
Now 

Pk = 3.6 X 10® 1^* Vk Nk mm per hour, (56) 

where Vk is the volume of a raindrop of k cm diam- 
eter, Vk is its terminal velocity in meters per second 
and Nk is their number per cubic centimeter. The 
attenuation of a rain of total precipitation rate p is, 
then, according to equation (54), 


OL\,p 


2 OL\{pk) = 
A = 0 


0.4343 VkQt.k 

3.6 Vuv, 

db per kilometer. 


(57) 


after substituting Nk from equation (56) into (54). 

For a given wavelength A, the ratio Qt,ic/yk'^k is a 
constant characteristic of drops whose diameter is k 
cm. This ratio will be denoted by qk. The attenuation 
formula then becomes, finally, 

8 

ap= 0.126 X Vkqki (58) 

* = 0 

which shows that the attenuation in rains of a total 
precipitation rate of p mm per hr depends linearly on 
the individual precipitation rates pk of all the drop 
groups k which build up this rain. The attenuation 
does not depend directly on the total precipitation 
rate p. The points representing the experimental ob- 
servations in the coordinate plane (a,p) should cover 
a certain region of this plane, but no single curve 
a(p) exists, since there is no direct relationship be- 
tween a and p. A curve drawn in this plane is sig- 
nificant only in so far as it permits one to predict a 
possible attenuation value in any rain of given pre- 
cipitation rate or vice versa. 

It is, however, possible to draw in the (a,p) co- 
ordinate plane a straight line which, at a given wave- 
length, will represent the theoretical upper limit for 
the attenuation. Indeed, using Table 6 for the attenua- 
tion in fictitious rains with a distribution of one drop 
per cubic centimeter, and Table 9, giving the precipi- 


tation associated with the same fictitious rains, one 
may compute the ratio «*//?& for any such rain formed 
by a single group of drops of diameter k cm and the 
precipitation rate pk of the same rain. This ratio for 
a given wavelength A of the radiation varies with k, 
the diameter of the drops; and in the diameter range 
0 to 0.55 cm this ratio takes on an optimum value for 
a certain diameter D. This, then, is the slope of the 
straight line in the {<x,p) plane which determines the 
theoretical upper limit amax of the attenuation in any 
rain of total rainfall p. 


Table 8. Precipitation rates p/N in fictitious rains 
with a concentration of one drop per cubic centimeter. 


Drop diameter D, cm 

p/N mm/hr 

0.05 

4.99 X 102 

0.10 

7.34 X 103 

0.15 

3.34 X 104 

0.20 

9.6 X 104 

0.25 

2.14 X 105 

0.30 

4.08 X 105 

0.35 

6.76 X 105 

0.40 

1.05 X 106 

0.45 

1.54 X 106 

0.50 

2.17 X 106 

0.55 

2.92 X 106 


The different steps taken in computing the total 
attenuation equation (58) in a rain of total rate of 
fall of p mm per hour appear in Figure 10 where the 
drop size distribution and the partial attenuations 
due to the different drop groups of a 22.6-mm per 



DIAMETER OF DROPS IN CM 

Figure 10. Drop size distribution and attenuation in 
a 22.6-mm per hr rain. Unlabeled curve represents Nk 
values; number of raindrops per cu m = A*. 


164 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


Table 9. Attenuation in rains of known drop size distribution and rate of fall (db/km). 


X, cm Distri- 


mm/hr 

1.25 

3 

5 

8 

10 

15 

20 

30 

50 

75 

100 

bution 

2.46 

1.93 10-1 

4.92 10-2 

4.24 10-3 

1.23 10-3 

7.34 10-4 

2.80 10-4 

1.52 10-4 

6.49 10-5 

2.33 10-5 

1.03 10-5 

5.85 10-6 

A 

4.0 

3.1810-1 

8.63 10-2 

7.11 10-3 

2.04 10-3 

1.1910-3 

4.69 10-4 

2.53 10-4 

1.0810-4 

3.88 10-5 

1.72 10-5 

9.75 10-6 

C 

6.0 

6.15 10-1 

1.92 10-1 

1.25 10-2 

3.02 10-3 

1.67 10-3 

5.84 10-4 

3.02 10-4 

1.25 10-4 

4.34 10-5 

1.93 10-5 

1.09 10-5 

D 

15.2 

2.12 

6.13 10-1 

5.91 10-2 

1.1710-2 

5.68 10-3 

1.69 10-3 

7.85 10-4 

2.95 10-4 

9.23 10-5 

4.1510-5 

2.35 10-5 

E 

18.7 

2.37 

8.01 10-1 

5.13 10-2 

1.10 10-2 

6.46 10-3 

1.85 10-3 

9.09 10-4 

3.60 10-4 

1.20 10-4 

5.36 10-5 

3.03 10-5 

F 

22.6 

2.40 

7.28 10-1 

5.29 10-2 

1.21 10-2 

6.96 10-3 

2.27 10-3 

1.1710-3 

4.81 10-4 

1.66 10-4 

7.41 10-5 

4.19 10-5 

G 

34.3 

4.51 

1.28 

1.12 10-1 

2.32 10-2 

1.1710-2 

3.64 10-3 

1.75 10-3 

6.83 10-4 

2.24 10-4 

9.95 10-5 

5.63 10-5 

H 

43.1 

6.17 

1.64 

1.65 10-1 

3.33 10-2 

1.62 10-2 

4.96 10-3 

2.29 10-3 

8.71 10-4 

2.78 10-4 

1.23 10-4 

6.98 10-5 

I 


lioiir rain are plotted. It is seen that the numerous 
smaller drops hardly contribute to the attenuation, 
which is caused mostly by the fewer larger drops and 
has a maximum around the 2.5-mm drops. 

In Table 9 is given the total attenuation (decibels 
per kilometer) in the wavelength range 1.25 to 100 
cm in different rains of precipitation rates ranging 
from 2.46 to 43.1 mm per hour corresponding to 
given distributions. In Figure 11 are plotted some 
curves showing, for a few rains, the variation of the 
total attenuation factor as a function of the wave- 
length. The dashed portions of these curves join the 



Figure 11. Attenuation in rains of known drop size 
distribution as a function of the wavelength. The 
abscissa gives the wavelength, X, in centimeters. The 
ordinate scale gives logic a, where the attenuation con- 
stant, or, is expressed in decibels per kilometer. The 
letters on the curves refer to the drop size distributions 
given in Table 7. 



Figure 12. (1) Computed K-band attenuation based 
on experimental drop size distributions. (2) Theoretical 
upper limit. o;/p=0.16 db /km/mm/hr. ^=18 C. 


points previously computed/^ the calculations start- 
ing at A = 5 cm. 

Figures 12, 13, and 14 represent, at three typical 
wavelengths, the total attenuations in ditferent rains. 
The results of the calculation are represented by the 
points indicated on these figures, and the smooth curve 
passing through these points serves to illustrate the 



Figure 13. (1) Computed X-band attenuation based 
on experimental drop size distributions. (2) Theoretical 
upper limit, a/p = 0.045 db/km /mm/hr. 18 C. 



ATMOSPHERIC ABSORPTION AND SCATTERING 


165 


procedure usually followed by the experimental work- 
ers, as we have already mentioned. It is evident that 
these curves have little, if any, direct physical signifi- 
cance. Similarly the curves of Figure 11 associated 
with different rains merely indicate the trend of varia- 



Figure 14. (1) Computed S-band attenuations based on 
experimental drop size distributions in different rains. 

(2) Theoretical upper limit of «/?>, attenuation per unit 
rate of precipitation, is 6. 10- ^db /km /mm /hr. t = 18C. 

tion of a as a function of the wavelength, since no 
single curve of this type can characterize a rain of 
given total precipitation rate of p mm per hour. 

Table 9 shows that the attenuation is of no practical 
importance for S band and longer waves even with the 
heeaviest rains or cloudbursts. This result is summar- 
ized in Table 10 (the theoretical upper limits of the at- 
tenuations per unit precipitation rate) . 


Table 10. Theoretical upper limits of attenuation 
per unit precipitation rate (i 18C). 


X, cm 

ia/p)max db/km/mm/hr 

1.25 

1.6 X 10-1 

3 

4.5 X 10-2 

5 

5.0 X 10-3 

8 

1.0 X 10-3 

10 

6.0 X 10-4 

15 

3.0 X 10-4 

20 

1.4 X 10-4 

30 

6.4 X 10-5 


These values in Table 10 correspond to raindrop 
temperatures of about 18 C. At lower temperatures the 
values of {<x/p) included in this table might be in- 
creased about 25 to 30 per cent. 

The results of the different workers in the field are 
summarized in Table 11. 

It will be seen that the above values of a/p compare 
favorably with the theoretical values.^ The difficulties 

^The same seems to be true of S-band wavelengths where 
rough attenuation measurements are available in “solid” 
storm clouds. 


Table 11. Experimental values of the attenuation 
per unit precipitation rate. 


X, cm 

(a/p) db/km/mm/hr 

Authority 

0.62 

0.37 

Mueller3 

0.96 

0.15 , 

Adam et 

1.089 

0.2 ' 

Robertson27 

1.25 

) 0.19 

Southworth et 

) 0.09—0.40 

Radoio 

3.2 

0.032—0.042 

King and Robertson30 


in the interpretation of the experimental data as men- 
tioned already should be kept in mind when compar- 
ing the experimental values with the theoretical 
predictions. 

As remarked by Eyde and Eyde,^^ the attenua- 
tion by hailstones and snow should be appreciably 
smaller than that due to raindrops, the dielectric con- 
stant of ice being considerably smaller than that of 
liquid water. 

A final remark may be made concerning the theore- 
tical results given here. It has been assumed through- 
out the preceding discussion that the raindrops are 
spherical. This is likely to be the case with practically 
all the drop groups existing in rains, with the excep- 
tion of the biggest drops, which may undergo deforma- 
tions. Presumably the effects of small deformations 
are not of great importance. 


10.1.7 'Yhe Scattering of Microwaves 
by Spherical Raindrops 

The cross section for scattering of electromagnetic 
waves by spherical particles is given for any direction 
by equation (34). Using the approximate expressions 
of the amplitudes as given by equations (38) and (43) 
and the notation represent- 

ing the real and imaginary coefficients of p® in 
of in etc., as indicated above, we get the fol- 
lowing expression for the total scattering cross sec- 
tion : 

+ ft ft P' + 6 [ft ft + ft <^> ft <«] p® 

+ |3[|ai(«r + lft<«h] 

+ 5|ft<«l2}p4 + 6[ft<»ft <® 

+ ft®ft<®]p5 + 3|ft<«pp'+--- 

Here, for instance, 

= y -f (a/'^)^ etc. 


I cm^. 

(59) 


166 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


For values of /3<^ 1 and when the terms in p~ and 
higher powers can be neglected in the braces, the 
total cross section for scattering reduces, using the ex- 
plicit expressions of and to 


Q 


s, p«l — 


1287r^a6 

3X4 


(Cr~ l)^(er+ + [2(6r — 1) (Cr H~ 2) +9] + 

[(g + 2)2+6,2]2 

When the dielectric absorption vanishes, i.e., 
this reduces further to 


ciiF. 

( 60 ) 

Ci-^O, 


Q. 


, P«i, 


1287r^a6 /n2 - 1\ 2 
3 X 4 (^^2 + 2 / 


cm2, 


( 61 ) 


which is the well-known Rayleigh scattering cross 
section, since e,- = ir in this case. 

In Table 12 are given the scattering cross sections 
computed within the range of p, 0.00157 to 0.576, or 
in the drop diameter range 0.05 to 0.55 cm and wave- 
length range 3 to 100 cm. Needless to say, the actual 
cross sections for scattering at the larger p values are 
always larger than the Rayleigh cross sections [equa- 
tion (60)]. For p < 0.10 the scattering cross sections 
are, within a few per cent, given by the first Rayleigh 
term (60) of equation (59). However, in the present 
case of absorbing spherical drops, the parametric 
representation (59) of the cross section is not of 
much practical interest since some of the coefficients 
of the powers of p are strongly dependent on the wave- 
length. The cross section is not a unique function of 
p = (ttD/X) but is a complicated function of A and 
71, and the series representation is valid only in de- 
scribing the dependence on the diameter D of the 
drops, the wavelength being kept constant. In Fig- 
ures 15 and 16 two families of curves have been 
plotted representing Qs as a function of the diameter 



0 IN CM 

Figure 15. Scattering cross section, Qs, of spherical 
water drops as a function of the drop diameter. The 
abscissa gives the drop diameter, D, in centimeters. 
The ordinate scale gives logio Qs, the scattering cross 
section Qs being expressed in square centimeters. The 
numbers on the curves indicate the wavelength, X, of 
the incident radiation in centimeters. 

D of the raindrops at constant wavelength and as a 
function of the wavelength at constant diameter, 
respectively. 

The knowledge of the total scattering cross section 
Qs and the total cross section Qt allows at once the 
computation of the absolute probabilities co^ for electro- 
magnetic waves falling on spherical water drops to be 


Table 12. Total scattering cross section Q^ (cm^) of spherical water drops of D cm diameter. 


X, cm 

0.05 

0.10 

0.15 

0.20 

0.25 

D, cm 

0.30 

0.35 

0.40 

0.45 

0.50 

0.55 

3 

3.62 10-8 

2.35 10-6 

2.74 10-5 

1.58 10-4 

6.06 10-4 

1.98 10-3 

5.36 10-3 

1.31 10-2 

2.96 10-2 

6.36 10-2 

1.31 10-1 

5 

4.70 10-9 

3.04 10-7 

3.51 10-6 

1.97 10-5 

7.56 10-5 

2.32 10-4 

5.97 10-4 

1.36 10-3 

2.86 10-3 

5.61 10-3 

1.04 10-2 

8 

7.23 10-10 

4.64 10-8 

5.35 10-7 

2.98 10-6 

1.1410-5 

3.44 10-5 

8.72 10-5 

1.96 10-4 

4.01 10-4 

7.65 10-4 

1.37 10-3 

10 

2.93 10-10 

1.88 10-8 

2.15 10-7 

1.21 10-6 

4.62 10-6 

1.38 10-5 

3.50 10-5 

7.85 10-5 

1.59 10-4 

3.01 10-4 

5.41 10-4 

15 

5.80 10-11 

3.75 10-9 

4.33 10-8 

2.43 10-7 

9.03 10-7 

2.70 10-6 

6.80 10-6 

1.52 10-5 

3.10 10-5 

5.87 10-5 

1.04 10-4 

20 

1.83 10-11 

1.1710-9 

1.35 10-8 

7.51 10-8 

2.86 10-7 

8.53 10-7 

2.1610-6 

4.81 10-6 

9.74 10-6 

1.83 10-5 

3.25 10-5 

30 

3.62 10-12 

2.32 10-10 

2.66 10-9 

1.49 10-8 

5.66 10-8 

1.69 10-7 

4.11 10-7 

9.51 10-7 

1.92 10-6 

3.62 10-6 

6.43 10-6 

50 

4.65 10-13 

2.99 10-11 

3.44 10-10 

1.91 10-9 

7.29 10-9 

2.1810-8 

5.51 10-8 

1.22 10-7 

2.48 10-7 

4.65 10-7 

8.27 10-7 

75 

9.22 10-14 

5.91 10-12 

6.79 10-11 

3.78 10-10 

1.44 10-9 

4.31 10-9 

1.08 10-8 

2.42 10-8 

4.91 10-8 

9.22 10-8 

1.63 10-7 

100 

2.93 10-14 

1.88 10-12 

2.15 10-11 

1.20 10-10 

4.56 10-10 

1.37 10-9 

3.45 10-9 

7.64 10-9 

1.56 10-8 

2.93 10-8 

5.20 10-8 


ATMOSPHERIC ABSORPTION AND SCATTERING 


167 



Figure 16. Scattering cross section, Qs, of spherical 
water drops as a function of the wavelength. The 
abscissa gives the wavelength, X, of the incident radia- 
tion in centimeters. The ordinate scale gives logic Qs, 
the cross section Qs being expressed in square centi- 
meters. The numbers of the curves indicate the drop 
diameter, D, in centimeters. 

scattered in any direction and the absolute probabil- 
ities for being absorbed by the drops, the absorbed 
energy being then transformed into heat in the drops 
(true absorption). Indeed, this probability co* of the 
waves being scattered in any direction is equal to the 
ratio of the scattering cross section Qs to the cross sec- 
tion Qt which is associated with all the possible even- 


tualities, here only two, namely, scattering and true 
absorption. Hence, 

= ^ (62) 

Qt 

and, consequently, the probability of true absorption is 
Wabs = 1 — COs. (63) 


In Table 13 are given the probabilities in the 
drop diameter range 0.05 to 0.55 cm and wavelength 
range 3 to 100 cm. A glance at this table shows that 
with the exception of the shortest wavelengths and 
largest drops the probability of the waves being truly 
absorbed is always much larger than that of their being 
scattered. The smaller the drops the greater the chance 
of absorption, since, according to the cross-section 
formulas, for small drops Qs is proportional to 
(Rayleigh’s law) whereas Qt'~~'Qabs is proportional 
to D^/\ and in our case the drop diameter D is always 
smaller than the wavelength A of the radiation. 

10.1.8 Back Scattering (Echoes) 

Whereas the attenuation of microwaves is of inter- 
est to both communication and radar, back scattering 
is of importance to radar only. The importance of the 
echo phenomena is twofold. On the one hand, it is 
of operational interest to distinguish between atmos- 
pheric echoes of the waves and their reflection from 
other targets in the atmosphere. On the other hand, 
the observation of these phenomena has led to the rec- 
ognition of its meteorological value in helping to map 
the storm topography of the atmosphere (storm detec- 
tion) around the position of the observer and at 
ranges limited only by the characteristics of the radar 
set used.^^'®^'®® 

The echo intensities may be computed from for- 
mula (35) for the differential cross section of drops 
o-(7r) for back scattering (scattering angle tt). 


Table 13. Probability of scattering co^ by spherical water drops of D cm diameter. 


X, cm 


D, cm 

3 

5 

8 

10 

15 

20 

30 

50 

75 

100 

0.05 

3.94 10-3 

1.64 10-3 

6.63 10-4 

4.25 10-4 

1.94 10-4 

1.09 10-4 

4.92 10-5 

1.74 10-5 

7.74 10-6 

4.33 10-6 

0.10 

1.54 10-2 

1.09 10-2 

4.89 10-3 

3.22 10-3 

1.53 10-3 

8.60 10-4 

3.91 10-4 

1.40 10-4 

6.33 10-5 

3.47 10-5 

0.15 

2.11 10-2 

2.90 10-2 

1.47 10-2 

9.96 10-3 

5.00 10-3 

2.87 10-3 

1.32 10-3 

4.73 10-4 

2.11 10-4 

1.17 10-4 

0.20 

2.86 10-2 

5.15 10-2 

2.91 10-2 

2.10 10-2 

1.11 10-2 

6.51 10-3 

3.05 10-3 

1.10 10-3 

3.95 10-4 

2.76 10-4 

0.25 

3.72 10-2 

7.60 10-2 

4.75 10-2 

3.16 10-2 

1.97 10-2 

1.21 10-2 

5.81 10-3 

2.14 10-3 

9.66 10-4 

5.37 10-4 

0.30 

5.31 10-2 

1.03 10-1 

6.91 10-2 

5.33 10-2 

3.12 10-2 

1.75 10-2 

9.77 10-3 

3.66 10-3 

1.61 10-3 

9.32 10-4 

0.35 

8.06 10-2 

1.29 10-1 

9.06 10-2 

7.28 10-2 

4.50 10-2 

2.96 10-2 

1.45 10-2 

5.76 10-3 

2.60 10-3 

1.47 10-3 

0.40 

1.21 10-1 

1.54 10-1 

1.13 10-1 

9.31 10-2 

6.C6 10-2 

4.11 10-2 

2.17 10-2 

8.42 10-3 

3.88 10-3 

2.18 10-3 

0.45 

1.95 10-1 

1.84 10-1 

1.35 10-1 

1.14 10-1 

7.79 10-2 

5.47 10-2 

2.96 10-2 

1.19 10-2 

5.50 10-3 

3.11 10-3 

0.50 

2.96 10-1 

2.17 10-1 

1.58 10-1 

1.34 10-1 

9.63 10-2 

6.88 10-2 

3.90 10-2 

1.59 10-2 

7.43 10-3 

4.23 10-3 

0.55 

4 82 10-1 

2.49 10-1 

1.80 10-1 

1.56 10-1 

1.15 10-1 

8.44 10-2 

4.95 10-2 

2.08 10-2 

9.82 10-3 

5.61 10-3 


168 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


According to equation (22), the power scattered by 
a spherical particle per unit solid angle at a point 
{r,6,(l>) is 


\do3/h<i> 2772 




(64) 


Using equations (16) and (17), we obtain, remember- 
ing that the incident power per unit area is ( 1/ 27^2) -E'o) 
the following expression for the differential scatter- 


ing cross section : 


( ^ \ 2 “ 


(2n + 1) (2m + 1) _ 
.it'i n{n + l) m{m + 1) 

[ / P^ dP^ \ 

anami -r— cos^^-f — — sin^ 0 1 
\ sin^ 6 dd do / 

/pi pi fipi ^pi \ 

+ 2a„ b* ^ cos^ 0 + 4^ sin^ 0 )1 cm^ 
Vsin 0 dd sin 0 dd /J 

(65)*^ 

Or, limiting ourselves to the approximation where only 
the electric dipole (&i), electric quadrupole and 
magnetic dipole (ctj are effective, we find, using the 
explicit expressions of the associated Legendre poly- 
nomials, 

(^-) =<r{0,<t>) 

\ do3 / <i> 

= (fj ■ 

Ref 9|6ip (sin^^ + cos^ d cos^ (f)) + 9| ai\^{cos^<l) 

+ cos^ d sin^ (f)) 

+ 25162!^ (cos^ d sin^ <j) -|- cos^ (2 d) cos^ 0) 

+ 18ai6i*cos0 + 3O6162* cos0(sin2<^ + cos {2d) cos^ cf)) 

+ 30 ai 62 * (cos^ d sin^ <j) + cos (2 d) cos^ </>) J cm^. ( 66 ) 

Here the first term inside the brackets represents the 
contribution of the electric dipole, the second is the 
magnetic dipole term, the third is the electric quad- 
rupole term, and the three others correspond to inter- 
ference terms between these three poles. 

In the optical case it is known that the larger the 
parameter p = irD/k^ i.e., the nearer the wavelength 
is to the diameter of the scattering sphere, the more 

•^With d = TT this reduces to equation (27) of the radar 
cross section. 


the radiation is scattered forward than backward. A 
study of equation (66) for water drops of 1-cm diam- 
eter shows that for spheres of this size it is only when 
X> 15 cm or p < 0.2 that the back-scattered intensity 
is about the same as the forward-scattered intensity. 
For such p values only the dipole term in equation 
(66) remains of practical importance. 

Suppose that we adopt a p value of 0.2 as a rough 
indication of what happens in the case of actual rain- 
drops, the diameter of which is less than about 0.55 
cm. It is then seen that for radar purposes the use of 
longer waves is favored, as far as the amount of back- 
scattered power is concerned, viz., in those cases where 
the greatest amount of back scattering from water 
drops is of operational importance. This will clearly 
occur in radar meteorology. However, when it is 
desirable to limit as much as possible the hack scatter- 
ing from rain or rainclouds, one might make use of 
this forward-backward scattering dissymmetry, which 
is the more pronounced the shorter the wavelength as 
compared with the diameter of the raindrops. This 
dissymmetry might, however, be counterbalanced by a 
rapid increase in the attenuation as well as a general 
decrease in the intensity of scattering. 

The differential cross section for back scattering re- 
sults from equation (66) by taking d = n there. Using 
the explicit expressions (43) of the amplitudes a^, 5i, 
and 1 ) 2 , one obtains for this back scattering (or radar 
cross section) 

0-(7r) p® (Ao + A2P^ + A3p'^-f A4P^+A5P®+A6P® 

^ +---)cm2, (67) 

with the following coefficients A”, using the notation 
defined by equations (45), (46), and (59) : 

Ao = 9|/3i(3)|2, 

A2 = 18 _ «/5)^/3)] 

-30[/3i(W^)+;di<W^)], 

A3= (68) 

A4 = 9 + 1/3/5) 1 2] - 18 [a/5)^/5) q_ ^/5)^/5)] 

- 30 [/3/5)/32(5) q_ ^/5)^2(5) _ q,/5)^2(5) 

-a/5);82<^)] + 25|/32<^)|2, 

A, = 18 _ «/5)^/6)] 

-30[i8/«))S2<^)+id/W5)]^ 

A6=91^/5)|2. 

The radar cross-section formula (67) is the same 
as that given by Ryde.^^ Again (r(7r) is not a function 


ATMOSPHERIC ABSORPTION AND SCATTERING 


169 


of p only since the coefficients of the successive powers 
of p in the expansion (67) depend on the wavelength. 
The computed echo cross sections o-(7r) for spherical 
water drops with diameters in the range 0.05 to 0.55 
cm and the wavelength range 3 to 100 cm are given 
in Table 14.^ These cross sections reduce practically to 
the Rayleigh type, i.e., the series (67) reduces to its 
first term for the smaller drops at any wavelength and 
for any drops for wavelengths larger than about 15 cm. 
Since the Rayleigh term predominates in o-(7r), with 
the exception of the larger drops and smaller wave- 
lengths, the trends of variation of o-(7r) with either 
the diameter, at constant wavelength, or the wave- 
length, at constant diameter, are similar to those of 
Qs, the total scattering cross section. A graphical repre- 
sentation of the data of Table 14 is thus of no particu- 
lar interest; they appear implicitly in Figures 15 
and 16. 

In order to compute the radar attenuation factor a 
associated with echo phenomena occurring with rain 
of known drop size distribution, we have but to use 
equation (31) and hence obtain for Njc drops of h cm 
diameter per cm®, 

0ir,k = ^Nk neper/cm, (69)™ 

and for a given distribution of particles 

s s 

2 i ^kW) neper /cm. (70) 

*=o ^ k=0 

Using the radar cross section of Table 14 and the drop 
size distributions in different rains as given in Table 

Tor the shorter waves and large drops the cross sections 
given are merely orders of magnitude, as the convergence of 
equation (67) is too slow in that case; in fact, it is even 
slower than the expression for Qs. 

“The coherent portion of the scattering is neglected here 
on account of the assumed random distribution of the scatter- 
ers. See, nevertheless, a recent note by F. Hoyle.®^ 



Figure 17. Absorption coefficient, 2^air, due to back 
scattering (echo) as a function of the wavelength in 
different rains. The abscissa gives the wavelength, X, 
in centimeters. The ordinate scale gives logio(2a7r), the 
absorption coefficient 2 0 ^ being expressed in km“i. 
The letters on the curves refer to the drop size distribu- 
tions listed in Table 7. 

7, we have computed a^, the attenuation factor due to 
back scattering in the wavelength range 3 to 100 cm. 
The results of these calculations are included in Table 
15 and in Figure 17. The variation of a^is represented 
as a function of the wavelength of the incident radia- 
tion in different rains of given drop size distribution 
and precipitation rate. As already emphasized in con- 
nection with the study of the attenuation, these curves 
are characteristic, probably, of those rains, but they 
are not unique, since a given rain of known precipita- 
tion rate might very likely be built up from a variety 
of drop size distributions. 

Since the absorption coefficient (2a^) for back scat- 
tering represents also the fraction of the incident power 


Table 14. Back scattering cross section <r (tt) (cm^) of spherical water drops of D cm diameter. 


X, cm 


D, cm 

3 

5 

8 

10 

15 

20 

30 

50 

75 

100 

0.05 

4.25 10-9 

5.55 10-10 

8.63 10-11 

8.50 10-11 

6.96 10-12 

2.18 10-12 

4.32 10-13 

5.60 10-14 

1.11 10-14 

3.50 10-15 

0.10 

2.64 10-7 

3.52 10-8 

5.47 10-9 

2.24 10-9 

4.44 10-16 

1.40 10-10 

2.77 10-11 

3.59 10-12 

7.09 10-13 

2.24 10-13 

0.15 

2.88 10-6 

3.97 10-7 

6.28 10-8 

2.54 10-8 

5.10 10-9 

1.60 10-9 

3.18 10-16 

4.12 10-11 

8.14 10-12 

2.57 10-12 

0.20 

1.48 10-5 

2.15 10-6 

3.45 10-7 

1.42 10-7 

2.84 10-8 

8.94 10-9 

1.77 10-9 

2.29 10-16 

4.52 10-11 

1.43 10-11 

0.25 

5.02 10-5 

7.42 10-6 

1.30 10-6 

5.34 10-7 

1.07 10-7 

3.42 10-8 

6.73 10-9 

8.72 10-16 

1.72 10-16 

5.45 10-11 

0.30 

1.34 10-4 

2.25 10-5 

3.80 10-6 

1.57 10-6 

3.19 10-7 

1.20 10-7 

2.02 10-8 

2.62 10-9 

5.17 10-16 

1.64 10-16 

0.35 

2.48 10-4 

5.40 10-5 

9.37 10-6 

3.91 10-6 

8.01 10-7 

2.58 10-7 

5.04 10-8 

6.53 10-9 

1.29 10-9 

4.08 10-16 

0.40 

5.04 10-4 

1.12 10-4 

2.03 10-5 

8.55 10-6 

1.77 10-6 

5.75 10-7 

1.13 10-7 

1.46 10-8 

2.88 10-9 

9.13 10-16 

0.45 

7.76 10-4 

2.12 10-4 

3.99 10-5 

1.70 10-5 

3.55 10-6 

1.16 10-6 

2.32 10-7 

3.00 10-8 

5.92 10-9 

1.87 10-9 

0.50 

9.91 10-4 

3.65 10-4 

7.30 10-5 

3.14 10-5 

6.63 10-6 

2.18 10-6 

4.32 10-7 

5.60 10-8 

1.11 10-8 

3.50 10-9 

0.55 

5.95 10-4 

5.82 10-4 

1.24 10-4 

5.44 10-5 

1.16 10-5 

3.87 10-6 

7.70 10-7 

9.98 10-8 

1.97 10-8 

6.24 10-9 


170 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


Table 15. Absorption coefficient due to back scattering (echo) 2ax km~i in rains of known drop size distribution and 
rate of fall. 


X, cm Distri- 


mm/hr 

3 

5 

8 

10 

15 

20 

30 

50 

75 

100 

biition 

2.46 

2.94 10-5 

4.21 10-6 

7.01 10-7 

2.86 10-7 

5.74 10-8 

1.82 10-8 

3.60 10-9 

4.66 10-19 

9.20 10-11 

2.91 10-11 

A 

4.0 

5.06 10-5 

7.31 10-6 

1.17 10-6 

4.81 10-7 

9.63 10-8 

3.03 10-8 

5.99 10-9 

7.76 10-10 

1.53 10-10 

4.85 10-11 

C 

6.0 

1.44 10-4 

2.32 10-5 

3.90 10-6 

1.61 10-6 

3.25 10-7 

1.17 10-7 

2.31 10-8 

2.99 10-9 

5.91 10-10 

1.87 10-10 

D 

15.2 

6.12 10-4 

1.73 10-4 

3.30 10-5 

1.41 10-5 

2.94 10-6 

7.62 10-7 

1.50 10-7 

1.94 10-8 

3.83 10-9 

1.21 10-9 

E 

18.7 

6.67 10-4 

1.27 10-4 

2.22 10-5 

9.25 10-6 

1.90 10-6 

6.51 10-7 

1.28 10-7 

1.66 10-8 

3.28 10-9 

1.04 10-9 

F 

22.6 

5.69 10-4 

1.01 10-4 

1.74 10-5 

7.24 10-6 

1.47 10-6 

4.91 10-7 

9.70 10-8 

1.26 10-8 

2.49 10-9 

7.88 10-10 

G 

34.3 

1.28 10-3 

3.02 10-4 

5.58 10-5 

2.36 10-5 

4.90 10-6 

1.63 10-6 

3.22 10-7 

4.17 10-8 

8.24 10-9 

2.61 10-9 

H 

43.1 

1.83 10-3 

4.89 10-4 

9.16 10-5 

3.90 10-5 

8.1410-6 

2.66 10-6 

5.26 10-7 

6.82 10-8 

1.35 10-8 

4.26 10-9 

I 


back scattered per unit thickness of the scattering 
medium, Tables 14 and 15 allow the computation and 
estimation of the echo power to be expected in radar 
observations under given conditions. The difficulties 
which seemed to exist earlier are cleared up by assum- 
ing that in those clouds which give rise to echoes pre- 
cipitation actually occurs, even though no rain reaches 
the ground.^® This is substantiated to some extent by 
recent work^® which succeeded in verifying Rayleigh’s 
law by observing cloud echoes simultaneously with 
both S- and X-band radar sets. Further proof was 
added by the Canadian group,^^ whose exhaustive 
study in the S band clearly showed the role of rain- 
drops in cloud echo phenomena. In fact, these workers 
stated that there was no record of an echo without rain. 

It is interesting to extract from Table 15 the frac- 
tion of the incident power back-scattered from differ- 
ent rains of 1-km depth expressed in decibels. As just 
mentioned, the power back-scattered by a thickness 
Aa; is 

AP. = -2a. Pi (71) 

and the fraction of the incident power Pi scattered 
backward by a layer A.t = 1 km is then 10 logjo ^P./ 
Pi db or (10 logio db (2aJ is given in Table 15. 
The results are included in Table 16. 

With Table 16 and the known sensitivity of a radar 
set, the maximum free space distance from the set at 
which these rains are observable can be computed at 


Table 16. Power scattered backward by a layer of 
1 km of rain in different rains (decibels). 


Distri- 

Vj 




X, cm 




bution 

mm /hr 

3 

5 

8 

10 

15 

20 

30 

50 

A 

2.46 

-45 

-54 

-61 

-65 

-72 ■ 

-77 • 

-84 

-93 

D 

6.0 

-38 

-46 

-54 

-58 

-65 

-69 

-76 

-85 

E 

15.2 

-32 

-37 

-45 

-48 

-55 

-61 

-68 

-77 

H 

34.3 

-29 

-35 

-42 

-46 

-53 

-58 

-65 

-74 

I 

43.1 

-27 

-33 

-40 

-44 

-51 

-56 

-63 

-71 


once. The peak power received by a radar set from 
Volume 3, Chapters 2 and 9, is 


P2 = PiGiG^ 





where P^ is the transmitted power (peak power), 

G^ and G 2 are respectively the transmitter and 
receiver antenna gains relative to a doublet, 
d is the distance of the set from the echoing 
rain drops, and 

is the back scattering cross section. 

The beam usually intersects the rain boundary and 
therefore it can be assumed that 8^ is made up of the 
combination of all the drops included in the echoing 
volume. This volume may be taken as a spherical shell 
of thickness ^d whose base is a spherical segment of 
area 


27 rc?^(l — cos B)y 

26 being approximately the half-power beam width of 
the set. 

The rain echo cross section is then 


S, = 2rd^ (1 - cos e) wj . 

Here the summation extends over all the different drop 
groups forming the rain and (Ti{Tr) is the differential 
cross section for back scattering in the direction tt with 
the direction of propagation of the initial beam. It 
should be remembered that o-i (tt) is the cross section per 
unit solid angle. Hence, the received peak power. 




for small 6 {6 in radians) . The quantity [%Ni(Ti( 7 r) Ad] 
is tabulated in Table 16 for = 1 km and the 
different rains of Table 7. It is thus clear that the 
knowledge of the set characteristics permits at once the 
computation of the received power echoed by a rain 
falling at a certain distance r from the set provided 


ATMOSPHERIC ABSORPTION AND SCATTERING 


171 


the assumption is made that the echoing rain layer is 
1 km thick. This is clearly arbitrary but is likely to 
give the right order of magnitude. 

There has been discussed in a rather unorthodox 
way^^ the elfect of the absorption on the back scatter- 
ing of radiation taking into account also the finite 
pulse length of the radiation source. 

These results seem to be consistent with the meager 
quantitative information available in this field. This 
fact would tend to classify the atmospheric radar 
echoes as back scattering phenomena due to water 
drops of precipitation size. It may further be re-em- 
phasized that theory provides an adequate explanation 
for scattering and absorption of electromagnetic waves 
passing through different clouds or precipitation 
forms. The limitations imposed on the theoretical re- 
sults are due essentially to irregularities inherent in 
the meteorological elements. 

Summary 

The present report gives a detailed review of the 
theoretical and experimental status of microwave at- 
mospheric absorption. This absorption is due to the 
gases of the atmosphere, oxygen, and water vapor, on 
the one hand, and to the swarms of floating or falling 
water drops, clouds, fog, rain, and snow, on the other. 

The status of the gaseous absorption of the atmos- 
phere is reviewed briefly in Section 10.1.1. Figure 1 
gives the oxygen and water vapor attenuation curves 
in the 0.2 to 10-cm wavelength range. The water vapor 
attenuation is given for a vapor content of 7.5 g/m^ 
of air, or 6.2 g per kilogram of air. In the equatorial 
belt, 15° S to 15° N, at sea level, the attenuation due 
to the atmospheric gases is approximately constant. It 
is about 0.18 and 0.008 db per kilometer for 1.25- and 
3-cm waves respectively. In the tropical region the 
seasonal variation of these attenuations is quite large. 

Figure 2 helps to give a clear picture of the atmos- 
pheric absorption due to oxygen and water vapor 
simultaneously with the absorption in rains of differ- 
ent types. It is seen that in the wavelength range 1 to 
5 cm the rain attenuation is more important than the 
gaseous atmospheric attenuation. The latter predomi- 
nates at waves shorter than 1 cm and longer than 
about 5 cm, losing entirely its practical importance 
at these longer waves. 

The theory of absorption and scattering of electro- 
magnetic waves by dielectric spheres (see Section 
10.1.2) is briefly presented following the Rayleigh 
method as developed by Stratton. 


The contribution of a swarm of spherical water 
drops of the same size, floating or falling in the atmos- 
phere, to the average field strength attenuation factor 
is given by 

a = ^NQt neper per unit length, 

where N is the average concentration of the drops, and 
Qt their total cross section. This total cross section is 
the ratio of the power removed from the incident beam 
by one drop, through scattering and internal absorp- 
tion to the power density of the incident beam. Similar 
definitions hold for the scattering cross section, absorp- 
tion cross section and differential cross section for 
back scattering or radar cross section. The total cross 
section Qt has the following form: 

Qt = ~ { — Re) 2- (2^+1) («n+^n), 

n = l 

where A denotes the wavelengths in free space of the 
incident radiation and and bn, {n = 1,2,3, • . .) form 
an infinite set of scattering amplitudes or coefficients 
associated with magnetic and electric poles of increas- 
ing order induced in the water drop by the field 
strengths of the radiation. Thus is associated with 
a magnetic dipole, b^ with an electric dipole, b^ with 
an electric quadrupole, etc. 

Section 10.1.3 is devoted to the study of the ampli- 
tudes an and These are complicated functions of 
the wavelength A, diameter D, or radius a of the drops, 
as well as the complex refractive index N or dielectric 
constant cc of water. Approximate expressions of the 
amplitudes can be derived by expanding them in series 
of ascending powers of the parameter p = ttD/X for 
p < 1. Retaining only terms up to we found the 
following expressions of the first amplitudes, 

3N^+2 \ 5N^+2 3N^+2'^J’ 

h - 5 

15 2N^+3 ’ 

where N is the complex refractive index of water with 
respect to free space and = €c = (cr — jej) is its 
complex dielectric constant. The numerical computa- 
tion of these amplitudes requires knowledge of the 
dielectric constant of water in the desired wave- 
length and temperature range. Whereas experimental 


172 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


data on the real part of the dielectric constant of water 
are relatively abundant in the microwave region and 
around 18 C, data on the imaginary part or the con- 
ductivity are very scarce. The Debye theory has, there- 
fore, been used to compute the dielectric constant of 
water in the microwave region, and the theoretical 
results seem to be supported by the new experimental 
data (see Table 1). Eecent data in the K band on 
the temperature variation of the dielectric constant of 
water are given in Table 2. The graphical representa- 
tion of both real and imaginary parts of the dielectric 
constant in the wavelength range 1 to 11 cm appears 
on Figure 4. The numerical values of a^, h^, and are 
discussed briefly at the end of this section. 

The attenuation factor (see Section 10.1.4) is here 
computed to the approximation of taking into account 
the amplitudes &i, and & 2 - Clearly, inasmuch as 
these amplitudes are expressed in the form of series 
in ascending powers of the parameter p = ttD/X, the 
attenuation factor takes on a similar form. One gets 

a = ^- (ci+C 2 p 2 + ) neper per unit length, 

20 X 

where m is the mass of liquid water in the form of 
drops per unit volume of the atmosphere, X is the 
wavelength of the radiation in free space, and Cg, 
c^, etc. are dimensionless coefficients depending on the 
wavelength implicitly through the dielectric constant 
of the substance of the sphere. For values of p small 
compared with unity, i.e., for waves long compared 
with the diameter of the drops, for which the terms 
in p^, p^, . . . can be neglected, the attenuation fac- 
tor reduces to one term, 

Sir mci 


= neper per unit length. 

10 X ier-\-2y+€^ 

This shows that for small drops or longer waves the 
attenuation factor becomes independent of the drop 
size and depends only on the amount of liquid water 
per unit volume present in the atmosphere. Table 3 
contains (in the 1- to 100-cm wavelength range) the 
values of the coefficients Ci, Cg, Cg. It also gives the 
critical drop diameters below which, for a given X, 
the one term attenuation formula holds within 10 
per cent accuracy. A few values of Dc are the fol- 
lowing : 

x.cm 1 1.26 *3 5 10 15 

Dc, cm 6.56X10-2 7.13X10-2 1.21X10-1 1.87X10-1 3.63X10-1 5.34X10-1 


Table 4 gives the total cross section of spherical 
water drops in the diameter range 0.05 to 0.55 cm 
and wavelength range 1.25 to 100 cm. Table 5 gives 
attenuation values in decibels per kilometer. Figures 
5 and 6 represent in graphical form the variation of 
the absorption cross section and attenuation factor 
( 1 ) at constant drop diameter, as a function of the 
wavelength, and (2) at constant wavelength, as a 
function of the drop diameter, respectively. 

These results are directly applicable to any pre- 
cipitation forms of which drop size distribution and 
average drop concentration have been determined. 

Meteorological data necessary to the computation 
of the attenuation factor of different precipitation 
forms have been collected in Section 10.1.5. Data on 
drop concentrations and drop size distributions are 
extremely scarce. 

In liquid water clouds of different altitudes and in 
fogs, observations indicate that the drop diameters do 
not exceed 0.02 cm. In low and medium altitude good 
weather clouds the liquid water concentration varies 
between 0.15 and 0.50 g per cubic meter, and a con- 
centration of 1 g/m^ is very likely an extreme upper 
limit. In fogs, with the possible exception of heavy 
sea fogs, the liquid water concentration seems to be 
considerably smaller. 

The data on drop size distribution in rains used in 
this work are given in Table 6, and, in a different 
form, directly applicable to the computation of the 
attenuation factor, in Table 7. These data indicate 
that the precipitation rate does not determine the drop 
size distribution of a rain, inasmuch as a rain of given 
precipitation rate can be built up with different drop 
size distributions. It does not seem, therefore, that 
the precipitation rate can play the role of a true phys- 
ical variable in the attenuation law of rains. 

Attention is also called to observed irregularities 
in the precipitation rate over relatively small dis- 
tances (about 1 km), which makes it difficult to in- 
terpret the experimental data on radio wave attenua- 
tions even in terms of this apparent variable of total 
precipitation rate. These and other meteorological 
irregularities seem to eliminate the possibility of a 
quantitative theory of attenuation or back scattering 
of radio waves by rain or other precipitation forms. 
Clearly, the experimental study of these as yet chaotic 
meteorological features might disclose certain trends 
which could be advantageously incorporated in the 
theory of attenuation of a stormy atmosphere. 

Figure 7 gives the empirical relationship between 
the terminal velocity of raindrops and their diameter. 


ATMOSPHERIC ABSORPTION AND SCATTERING 


173 


The measurements cover practically the whole range 
of drops which reach the ground in rains, or from 0.05 
to 0.55 cm. The terminal velocity of these drops varies 
between 2 and 9 m per second approximately. Figure 
8 represents another empirical relationship between 
the liquid water concentration of the rainy atmos- 
phere and the rate of rainfall. A rough linear approxi- 
mation to the apparent empirical curve leads to a 
water content 0.038 g/m^ for each millimeter per 
hour precipitation rate. But, strictly speaking, there 
cannot be an analytical connection between the liquid 
water concentration and the rate of rainfall. Inasmuch 
as the same rate of rainfall can be achieved by a num- 
ber of different drop size distributions, therefore, to 
a single value of the abscissa — the precipitation rate 
— there may be associated a series of ordinate values 
or liquid water concentrations. The curves of Figure 
8 are, therefore, of interest only because they are 
helpful in predicting very roughly liquid water con- 
centrations in different rains. 

The subject of Section 10.1.6 is the computation of 
the attenuation in different precipitation forms, no 
account being taken of the inherent irregularities. 

Since the size of the drops in fogs and fair weather 
clouds are small compared with even the shortest wave- 
length (1.25 cm) considered in this report, the one 
term attenuation formula holds rigorously. Figure 9 
represents the attenuation curve in decibels per kilo- 
meter in clouds and fogs for a liquid water concentra- 
tion of 1 g/m^ which, as mentioned above, is an upper 
limit. 

A few attenuation values may be given as follows: 

X, cm 1.25 3 5 10 

a/m db/km/gm/m3 0.28 0.049 0.018 0.0045 

Even for 1.25-cm waves the attenuation would be- 
come important only at long ranges for radar observa- 
tions. For waves of length A > 3 cm the attenuation 
in fair weather clouds and fogs is of no practical 
importance. 

Table 3, on the critical diameter of water drops, 
shows that the attenuation becomes practically in- 
dependent of the drop size distribution in rains for 
wavelengths longer than about 15 or 20 cm, inasmuch 
as raindrops whose diameter is larger than 0.55 cm 
or 0.6 cm do not reach low altitudes. In the 5- to 20- 
cm wavelength range the three-term attenuation 
formula will represent fairly well the attenuation in 
different rains. At wavelengths smaller than 5 cm 
exact computations of the amplitudes hn are nec- 
essary. 


It is shown that in any rain the attenuation de- 
pends linearly on the partial precipitation rates of 
the different drop groups making up this rain, but 
it does not depend directly on the total rate of rain- 
fall. 

Figure 10 purports to show the connection between 
the drop size distribution in a given rain and the 
partial or fractional attenuation values in the K and 
X bands of the different drop groups making up this 
rain. It is seen that the numerous small drops do not, 
for practical purposes, contribute to the attenuation, 
which is due mainly to the bigger drops. 

Table 9 contains attenuation values of different 
rains of known drop size distribution and rate of rain- 
fall. Figure 11 is a graphical representation of these 
results. It will be seen that at the shorter waves the 
attenuation may become important in heavy rains. 

Figures 12, 13, and 14 are graphical representa- 
tions of certain results included in Table 9 at K-, 
X-, and S-band wavelengths, respectively. The attenua- 
tion values corresponding to the points in these graphs 
have been computed for the rains of Table 9, and we 
have drawn a curve through the computed points. 
Accordingly, the plot of attenuation as a function of 
total precipitation is a mass plot. That is, for any 
given total precipitation the attenuation will have 
different values, depending upon the distribution of 
the drop size for the rain in question. Figures 12, 
13, and 14 represent mass plots of the meager data 
available for K, X, and S bands, respectively, together 
with the limiting curve that would result if all the 
drops were of the size that gives maximum attenua- 
tion. Tables 10 and 11 contain, respectively, the theo- 
retically predicted upper limits of attenuation for 
water drops around 18° C and the experimental atten- 
uation per unit rate of precipitation. In view of the 
difficulties in the interpretation of the experimental 
data, it may be said that there is fair agreement be- 
tween the observed and predicted attenuation values 
in rains. 

The attenuation due to hailstones and snow should 
be considerably smaller than that caused by rain. The 
reason for this difference is due to the small dielectric 
absorption of ice as compared with the dielectric ab- 
sorption of liquid water. 

Section 10.1.7 deals with the total scattering (in 
the whole solid angle) of microwaves by spherical 
water drops. The scattering cross-section formula is 
given in a series of ascending powers of p = ttD/X, 
the first term of the series being p®. For small 


174 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


values of p, the cross section reduces to the first term 
of this series, which, when the dielectric absorption 
is negligible, reduces to the Rayleigh scattering cross 
section. Table 12 includes the results of the numer- 
ical computations and Figures 15 and 16 are their 
graphical representation. 

The knowledge of the total cross section and scat- 
tering cross section allows the computation of the 
absolute probabilities for the waves to be scattered 
in any direction or to be absorbed internally by spher- 
ical water drops. The scattering probabilities are 
given in Table 13. The probabilities for internal ab- 
sorption are complementary to these, i.e., they are 
equal to (1 — ) . It is thus seen that, with the 

exception of the shortest waves and the biggest rain- 
drops, the probability of the waves being absorbed in- 
ternally, the absorbed wave energy heating the drops, 
is much larger than the probability of their being 
scattered in any direction. 

In Section 10.1.8 the differential scattering cross 
section in a chosen direction is first derived rapidly and 
then is given explicitly so as to show clearly the con- 
tributions of the induced electric dipole, electric quad- 
rupole, magnetic dipole, and their interference terms. 
Attention is here called to the already well-known 
fact that in the optical spectrum region dissymmetry 
appears in the angular distribution of the scattered 
radiation. That is to say, the larger the parameter p 
or the nearer the drop diameter to the wavelength, the 
greater the power scattered in the direction of the 
propagation in comparison with that scattered back- 
ward or at 180° to the direction of propagation. 

The back-scattering cross section or radar cross 
section of water drops is given in the form of a series 
in ascending powers of the parameter p. Table 14 
contains the results of numerical computations of 
these radar cross sections for water drops in the diam- 
eter range 0.05 to 0.55 cm and wavelength range 3 
to 100 cm. 

The radar cross section allows the determination 
of a radar attenuation constant. The radar absorp- 
tion coefficient, or the double of the attenuation con- 
stant, is the fraction of the incident power scattered 
backward by a layer of unit thickness of the echoing 
medium. Table 15 contains the numerical values of 
this radar absorption coefficient in different rains of 
known drop size distribution, and Figure 17 is its 
graphical representation. Table 16 is a somewhat 
modified form of Table 15, in so far as it gives in 
decibels the fraction of the incident power scattered 


backward by a 1-km layer of different rains. The 
theoretically predicted back scattering seems to be 
in fair agreement with the rather few experimental 
data on the power received in radar observations of 
rains or rain clouds. 

In conclusion it may be stated that, in view of the 
scarcity of meteorological data and the irregularities 
inherent in meteorological phenomena, the theory 
provides a satisfactory picture of the propagation of 
microwaves through a variety of precipitation forms 
present in the atmosphere. 

K-BAND ABSORPTION — 
EXPERIMENTAL^ 

Our knowledge of the attenuation of K-band radia- 
tion in the normal atmosphere is based upon the 
theory outlined by Van Vleck and upon a number of 
experiments, some of which were undertaken to ob- 
tain data needed in the theory, others of which were 
attempts to measure directly absorption by the at- 
mosphere. 

The width of the rotational lines of water vapor in 
the infrared has recently been measured in work at 
the University of Michigan. The width of the oxygen 
lines responsible for the strong absorption at 0.5 cm 
and the rather small effect at K band are inferred 
from experiments at the Radiation Laboratory. The 
absorption in oxygen was measured directly at sev- 
eral wavelengths in the neighborhood of 0.5 to 0.6 
cm. The gas was contained in a wave guide about 6 m 
long. This guide could be evacuated and then filled 
with gas to any desired pressure between zero and 
roughly 1,000 mm Hg. The radiation was obtained 
as the second harmonic generated in a crystal rectifier 
fed by a K-band oscillator. The source was amplitude 
modulated at audio frequency, and the signal was 
detected by a second crystal at the far end of the 
wave-guide path. The attenuation in the gas was de- 
termined by comparing the signal received with the 
guide evacuated to that received with gas present in 
the guide. The absorption of pure oxygen, at various 
pressures, as well as that of controlled mixtures of 
oxygen and other gases, was measured. The results 
confirm the predictions of the theory in a very con- 
vincing manner and suggest a value of the line width 
lying between 0.05 and 0.02 cm“^. 

Direct measurements of atmospheric absorption 
at K band have been made by a group at the Radia- 

“By E. M. Purcell, Radiation Laboratory, MIT. 


ABSORPTION OF K-BAND RADIATION BY WATER VAPOR 


175 


tion Laboratory using a K-band radar set in an air- 
plane. For this purpose, the set was provided with 
fixed attenuators which could be switched in or out 
of the system. Both r-f and i-f attenuators carefully 
calibrated were used. The experiment consisted in 
flying a straight level course away from a known 
target and determining the maximum range to which 
the target could be seen with and without attenuation 
in the system. The maximum ranges involved were of 
the order of 30 miles. From the results a value for 
the attenuation in the atmosphere can be calculated, 
assuming free space propagation, and this value in 
turn correlated with the meteorological data. The 
latter were obtained from radio-sonde flights at MIT. 

After making allowance for the rather small oxygen 
effect, the results are best represented by a figure of 
0.02 db per nautical mile for 1 g/nF of water vapor. 
In several of the flights the target was an accurately 
made 4-ft corner reflector. This provides an independ- 
ent upper limit to the attenuation, since all system 
parameters (antenna gain, S/N, etc.) were known, and 
one can calculate how far the corner should have been 
seen with any supposed amount of atmospheric atten- 
uation. The upper limit estimated in this way is about 
0.04 db per nautical mile for 1 g/m^ of water vapor. 

An entirely different method for measuring attenu- 
ation in the atmosphere has been developed at Eadia- 
tion Laboratory. It is possible to measure the apparent 
radiation temperature of any matched r-f load, includ- 
ing an antenna, with great precision ' 1C). In the 
case of an antenna, the temperature measured is the 
temperature of whatever the antenna is looking at, 
that is, the temperature of whatever would absorb the 
energy emitted from the antenna if the antenna were 
transmitting. When the antenna is pointed at the sky, 
the temperature measured is some mixture of the tem- 
perature of outer space and the temperature of the air, 
the influence of the latter being determined in a direct 
and simple manner by the absorption coefficient of the 
air layer. From measurements of the apparent tem- 
perature of the sky at various elevation angles, the 
total absorption in decibels for a vertical path through 
the entire atmosphere can be deduced. The data which 
have been collected in this manner show good internal 
consistency; assuming that the MIT radio-sonde data 
give the total water vapor in the atmosphere correctly, 
a value of 0.04 db per nautical mile for 1 g/m® is ob- 
tained for the water vapor attenuation. This is larger 
than the other value quoted above. The reason for the 
discrepancy is not yet known. 


ABSORPTION OF K-BAND 
RADIATION BY WATER VAPORS 

An experiment to determine the location and shape 
of the water vapor absorption line in the K-band 
region of the electromagnbtic spectrum is in progress. 
The experiment consists in the measurement of the 
change in Q of k large copper box when water vapor is 
introduced. From this change in Q the loss by absorp- 
tion in the water vapor can be determined and hence 
the attenuation of K-band radiation in water vapor. 

The experimental setup consists of an approximately 
cubical (but irregular in terms of A) copper box of 
15.8 cu m volume. Energy from a pulsed magnetron 
is fed into this box through a wave guide which ter- 
minates in a matched horn facing a rotating copper 
fan placed in the roof of the box. The purpose of this 
fan is to stir up the standing wave pattern in the box. 
Throughout the interior of the box are placed strings 
of Chromel-constantan thermocouple junctions sealed 
in 707 glass tubing. Alternate junctions are coated 
with a mixture of polystyrene and iron powder. In all, 
there is a total of 220 painted or ‘^hoF’ junctions in the 
box. Provision is made for introducing water vapor 
into the box and for circulating the air. The tempera- 
ture is maintained at 45 C during all runs, and the 
pressure is atmospheric (760 dz 15 mm, depending on 
conditions). An aperture of area 400 sq cm which may 
be opened or shut by means of a sliding copper door is 
located in one side of the box. Radiation entering the 
box is absorbed by the walls, by the paraphernalia in 
the box, by the gas, by the apertures (if any), and by 
the thermocouple junctions. The coated thermocouple 
junctions absorb more energy than the uncoated junc- 
tions and a net emf is produced. A single junction 
would give an emf proportional to the value of the 
square of the electrical field at its position, but the 
reading would be very sensitive to the location of the 
couple and, even if this were held fixed, would be sen- 
sitive to* small deformations of the walls. The large 
number of the couples actually used averages the value 
of the square of the electric field, E^, over the entire 
box, and the fan previously mentioned assists in this 
averaging. The Q of the box and its contents is, for 
constant magnetron power output, proportional to W 
and thus to the emf of the thermocouples. 

Since the couple emf is also proportional to the 
power output of the magnetron, changes in the output 
power will show up in the results in the same way as 

®By J. M. B. Kellogg, Columbia University Radiation 
Laboratory. 


176 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


changes in Q, Original difficulties arising from this 
cause, which were encountered because of variation in 
the a-c line voltage and the modulator voltage, have 
been largely eliminated by the use of stabilizing trans- 
formers and a magnetron load current stabilizing cir- 
cuit. Furthermore, a method of taking data was de- 
vised which only required the power output to be 
maintained constant for a few minutes at a time. 

The Q of the water vapor, Qy, is given by 



(72) 


where y is the attenuation in db per nautical mile, A 
is in centimeters, and K is a constant. In order to 
obtain absolute values of the attenuation, it is necessary 
to introduce into the system a known Q in terms of 
which the other §’s may be evaluated. For this purpose, 
the aperture, which acts as a perfect absorber, is used. 

Lamb has derived a formula for the Q of an aper- 
ture, Qa, and this is 


J_ - 

Qa ~ SttF ' 


(73) 


where A is the area of the aperture and V is the volume 
of the box. 

The Q of the whole ensemble may now be written 
down. 


1 _ J_ J_ J_ 
Q~ Qb'^ Qv'^ Qa’ 


(74) 


where Qb takes account of all losses (including the 
losses in oxygen) other than those in the vapor and 
the aperture. Inserting values, and using l/rj as the 
proportionality constant connecting the emf, (f, and 
Q, one then has 


For constant conditions of humidity, wavelength, and 
magnetron power output, measurements are now made 
of the emf (fo, with A = 0, and emf ^a, with A = A. 
Using these measured values of emf, equation (75) 
can be written in the form 






8tV / 1 

XA \Qb 


A- Ky\ 


)= 


(76) 


The humidity is then changed and the measurement 
repeated until enough points have been obtained to 
provide a curve of F as a function of p, the water vapor 
density, for constant wavelength. 


Since, presumably, y is the only quantity in this 
equation which is a function of p, and since y = 0 for 
p = 0, the plot of F against p extrapolated to zero 
humidity will yield a value of Qb. Consequently, y is 
determined as a function of p. 

Examples of the y versus p curves so obtained are 
shown in Figure 18 for the wavelengths 0.96, 1.16, 
1.28, and 1.69 cm. Data were also taken at the wave- 



/O IN G PER CU M 

Figure 18. Attenuation in water vapor. 

lengths 1.06, 1.31, 1.37, and 1.49 cm. These lines are 
all concave upward with the exception of those at 
1.28, 1.31, and 1.37 cm. There is some evidence that 
the line at 1.31 cm is concave downward, while within 
experimental error the 1.28- and 1.37-cm lines are 
straight. 

The curvature is surprising, since it was believed 
that y would be proportional to p. The reason for the 
curvature is not understood, and it is possible that it 
arises from some systematic experimental error. How- 
ever, it is difficult to conceive of a systematic error 
which disappears at resonance. 

Because of this curvature, it is not possible to draw 
a single attenuation curve showing absorption as a 
function of wavelength for all humidities. Figure 19 
shows the variation with wavelength of the attenuation 
coefficient y/p in decibels per nautical mile per gram 


K-BAND ATTENUATION DUE TO RAINFALL 


177 



of water vapor per cubic meter for humidities of 10 g 
per cubic meter and of 50 g per cubic meter. It is to 
be noted that the peak of this curve, at 1.32 cm, is 
very close to the standard K-band wavelength. 

These experimental results are in agreement with 
other results for the water vapor attenuation at K 
band. Furthermore, for all practical radar purposes, 
and within the range of the measurements, they are 
in agreement with Van Vleck’s theory of the absorp- 
tion of this water vapor line. 

Discussion 

Comments were made on the great accuracy of the 
experiment, pointing out that the quantity being 
measured was extremely small and that other experi- 
ments, particularly one made in Florida by measure- 
ment of the sky temperature, were leading to substan- 
tial agreement with the present findings. The best 
available data on the performance of K-band radars 
supported the experimental result obtained and would 
be of great help in choosing wavelengths for radar and 
other apparatus in the future. 

The good agreement between theory and the experi- 
mental result achieved was stressed. Whereas in infra- 
red absorption measurements the results had disagreed 


with theory by as much as 10 db or more, the discrep- 
ancy in these results amounted to a few per cent only. 
It was noted that from the purely physical standpoint 
this water vapor line and the 0.5-cm oxygen absorption 
line were the most carefully investigated lines in the 
spectrum, aside from somb lines in the visible region. 
The explanation was given that the microwave meas- 
urements were much more instructive than the optical 
ones from the standpoint of the collision broadening 
theory because the width of the microwave absorption 
line was comparable to the frequency of the radiation. 
This results in a shape factor or line form which can 
be studied in detail. The reported dependence on den- 
sity presents a difficult problem which is not yet well 
understood. 

The practical importance of the curvature shown in 
Figure 18 was emphasized. It was pointed out that 
the effects of a wide range of humidities had been in- 
vestigated, some very high compared to those ordi- 
narily encountered. In practical work most of the data 
Avonld be obtained from the low end of the curves of 
Figure 18, where little ambiguity in numerical values 
would obtain. 

10 4 K-BAND ATTENUATION DUE TO 
RAINFALLP 

Introduction 

In order to determine the attenuation of 1.25-cm 
wavelength radiation by rain, controlled radio and 
meteorological measnrements were undertaken in an 
area providing adequate climatic conditions for the 
study. It was apparent that the attenuation measure- 
ments should be made in an area of maximum precipi- 
tation for expediency. Furthermore, the experiment 
demanded periods of varying rates of rainfall with fre- 
quent ^^clearing’^ for calibration purposes. Tropical 
orographic (mountainous) rain seemed to offer the 
greatest probability of fulfilling these conditions. 

A brief reconnaissance of the Hilo, Hawaii, area 
showed that a site near Kaumana was adequate, hav- 
ing a yearly fall in excess of 250 in., as compared with 
an annual rainfall of 10.10 in. in the San Diego area. 
A 1.21 statute mile link was chosen parallel to the 
mean trade wind vector, i.e., due east-west, and was 
located on a lava fiow of 1881. The lava was covered 
with saw grass and low brush. The terrain had a gentle 
slope from the receiver at 2,500 ft to the transmitter 
at 2,800 ft above mean sea level. 

PBy L. J. Anderson, U. S. Navy Radio and Sound Lab- 
oratory. 


178 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


10.4.2 Rainfall Intensity 

Orographic lifting of the unstable moist tropical 
air caused frequent 2 - to 3-day periods of precipitation 
having a wide range in intensity. On one occasion in- 
tensities as high as 125 mm per hour were observed. 
Due to the light winds associated with orographic 
precipitation an essentially vertical trajectory of the 
raindrops was obtained ; and, therefore, representative 
sampling of the rain falling through the radiated 
energy path was accomplished by placing the gauges 
directly in line between the transmitter and receiver. 

Although the rainfall intensity varied widely both 
with time and in space, well-coordinated measuring 
techniques having sufficient coverage detected periods 
when the rate of fall along the path was uniform. 
Since such periods of uniformity seldom lasted longer 
than 60 sec, precise control and timing were vital. Two 
methods of determining the rate of precipitation were 
employed. Five Julien Friez tipping-bucket automatic 
recording rain gauges were evenly dispersed along the 
path and their signals were recorded on a single 
Esterline-Angus five-pen recorder at the receiver sta- 
tion. In addition, four rain shelters employing the 
‘Tunnel and graduate” technique were installed be- 
tween the automatic gauges as shown in Figure 20. 
The rain shelters were provided with field phones for 


ATTENUATION PATH 



X automatic rain gauge Orain shelter 

Figure 20. Layout of experimental path and apparatus. 


TRANSMITTER 


receiving instructions as well as simultaneous signals 
for taking graduate readings and exposing drop size 
blotters. During operations, signals for graduate read- 
ings were given every 30 sec. Blotters for drop size 
measurements were simultaneously exposed on an 
average of every 5 min. 

10.4.3 Radio Equipment 

The equipment used for the attenuation measure- 
ments is shown in Figure 21. It was relatively simple 
and required little attention once the initial warm-up 
drifts were stabilized. The technique for a satisfactory 
measurement involved a comprehensive check of the 
“clear weather” values before and after any one rain- 
fall. 

The transmitter was housed in a small elevated 
shack and the antenna and guide were protected from 
the rain by a back-sloping shutter flap. 

A 2K33 tube, modulated with 800 c, was used as the 
transmitter. Wave-guide feed was employed on a 2-ft 
paraboloid antenna (beam width 1.7°). A thermistor 
with a directional coupler was used as a power 
monitor. 

A 2-ft paraboloid collected energy at the receiving 
end and fed the receiver through a wave guide. A 
superheterodyne utilizing a 2K33 local oscillator drove 
a 30-mc i-f amplifier with 6-mc bandwidth. The second 
detector output fed an audio amplifier and recorder. 

A signal generator was used to check the receiver 
characteristic. This generator consisted of a 2K33 
tube and two flap attenuators. Fixed pads were used 
on either side of the flap attenuators to provide a flat 

SIGNAL GENERATOR RECEIVER 


MONITOR 

thermistor 


|bridge 1 — H 


DIRECTIONAL 
COUPLER 



;-FT PARABOLOID 


POWER 
SUPPLY AND 
MODULATOR 



Figure 21. Block diagram of K-band attenuation measurement apparatus. 



K-BAND ATTENUATION DUE TO RAINFALL 


179 


line. The characteristics of the flap attenuators were 
checked every few hours, using a K-band thermistor. 
Each flap was calibrated and used over a 12-db range. 
Eesettability was approximately ±0.1 db. A small 
nozzle was used to direct the output of the signal gen- 
erator upon the receiving paraboloid. Calibrations 
were made before, during, and after rainfalls and were 
within ±1.0 db over the 5- and 6-hour measuring 
periods. 

Analysis 

The primary attenuation curve of Figure 22, shown 
with solid dots, was obtained by choosing periods when 
the rainfall at all stations, including the automatic 
gauges, was essentially uniform. Six such periods of 



Figure 22. Primary attenuation curve of K-band 
radiation in rain. K-band attenuation versus rainfall 
intensity. (Note: Decibels per nautical mile.) 


60 r 



DISTANCE ALONG PATH 


Figure 23. Profile of rain intensity along the path. 
Time 223645. 

uniform fall along the path were selected covering the 
important range of 0 to 41 mm per hour. Figure 23 
is a rainfall intensity profile of the highest uniform 
fall recorded. By Humphreys’ classification of rain<* 
the intensities covered by the primary curve are more 

^1 mm per hour, light rain; 4 mm per hour, moderate rain; 
15 mm per hour, heavy rain; 48 mm per hour, excessive rain. 
See reference 24. 


than adequate for normal rates of precipitation en- 
countered in nature. 

Using the primary attenuation curve thus obtained, 
it was possible to extend the curve for extremely high 
rates of fall (cloudbursts) in the following manner. 
Figure 24 is a rain intensity profile at an interval of 



Figure 24. Intensity profile during uneven precipita- 
tion. Time 171115. 

nonuniform rainfall distribution. The area under the 
curve is divided into sections as shown. These sections 
cover the portions of the path where the intensity was 
below 41 mm per hr. Hence with the primary attenua- 
tion curve and a planimeter it is possible to assign the 
contribution that each section makes to the total ob- 
served attenuation (assuming that the attenuation in 
decibels is linear with distance) . 

After subtracting out the part of the attenuation 
already known, the high intensity central portion is 
left to account for the residual attenuation. Dividing 
the residual attenuation by the fraction of a mile cov- 
ered by this part of the path and plotting this value 
against the average intensity in the interval gives a 
point at 78 mm per hour. As a check on the method, 
similar profiles were worked up which gave points 
below 40 mm per hour. These are plotted as open cir- 
cles, as shown in Figure 22. It will be seen that the 
open circles agree quite well with the solid ones, 
and hence considerable confidence in the high inten- 
sity points is justified. 

Discussion 

The total observation time of the experiment was 
roughly 3 hours, about half of this total time being 
represented by the figures presented with the paper. 
It was necessary to employ a large number of precipi- 
tation measuring stations along the path in order to 
obtain an accurate precipitation profile. Some inci- 
dental work on drop size was also done. The spread 
in drop size at a given time was rather large, probably 


180 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


because of the orographic character of the precipita- 
tion, which was made up of drops falling on the aver- 
age not much more than 1,000 ft, as compared to ordi- 
nary rain falling 5,000 to 6,000 ft. The longer period 
of fall in ordinary rain probably permits a greater 
number of drops to reach the characteristic sizes. 

105 ABSORPTION OF MICROWAVES BY 
THE ATMOSPHERE, BRITISH WORK^ 

The working committee of the Ultra Short Wave 
Panel has presented a report in which the following 
questions are treated in detail : 

1. The absorption of microwave radiation by oxy- 
gen and vapor. 

2. The absorption of microwave radiation by water 
in macroscopic form, for example, rain, clouds, fog. 

3. The measurement in the laboratory of dielectric 
constants and conductivity which have already been 
described (see Section 9.3). 

The work under item (1) consisted chiefly in show- 
ing that the attenuation given by Telecommunication 
Research Establishment radar experiments at Llan- 
dudno at a wavelength of 1.25 cm was consistent with 
the theoretical values given in reference 1. The experi- 
mental method consisted of comparing the echoes re- 
ceived on X- and K-band radars from a standard re- 
flector at short range and from land echoes at a large 
range. Care was taken to insure that the reflecting tar- 
gets did not reflect an amount of energy which was 
dependent on frequency. In this way a minimum value 
for the attenuation on \ = 1.25 cm was found to be 
0.14 db per kilometer. New values based upon revised 
values of the widths of the various lines of water vapor 
and oxygen show that almost the whole of this atten- 
uation must be due to absorption by water vapor and 
further that to obtain an absorption as high as 0.14 
db per kilometer the frequency at the important water 
vapor line must lie close to 1.25 cm. 

The work under item (2) has been carried out, in 
the case of rain, by assuming what seemed a plausible 
distribution of drop sizes and calculating on this basis 
the attenuation that would occur at a standard pre- 
cipitation rate. Then by making a climatological sur- 
vey, information can be given of the proportion of 
time during which the attenuation can be expected 
to exceed a given value for a radar or radio commu- 
nication set working on a given wavelength at a given 

'By F. Hoyle, Ultra Short Wave Panel, Ministry of Supply, 
England. 


location. The calculations for a standard precipita- 
tion rate gave the following estimates for the maxi- 
mum attenuation likely to occur (that is, for the 
most unfavorable drop size distribution that was 
thought likely to occur). 

S band: 0.003 db per km per mm per hr. 

X band : 0.06 db per km per mm per hr. 

K band : 0.22 db per km per mm per hr. 

The climatological part of the program involves a 
great deal of statistical work and is not yet complete. 
The following preliminary results can be given. 

At Padang in Sumatra w^e may expect, twelve times 
a year, periods of 1 hr when the average attenua- 
tion on 1.25 cm will be some 6 to 12 db per kilometer; 
on 3.0 cm, 2 to 4 db per kilometer; and on 10 cm, 0.1 
to 0.2 db per kilometer. 

In England only once a year will the average at- 
tenuation over a period of one hour reach 1 to 2.5 db 
per kilometer on 1.25 cm; 0.3 to 0.8 per kilometer 
on 3.0 cm; and 0.02 to 0.04 db per kilometer on 
10.0 cm. 

It should be noticed that these attenuation figures 
are for point-to-point communication and must be 
doubled in the radar case. 

10 6 DIELECTRIC CONSTANT AND LOSS 
FACTOR OF LIQUID WATER AND 
THE ATMOSPHERE^ 

In propagation problems the knowledge of the 
electric properties of the ground, sea, and fresh water, 
as well as those of the atmospheric gases, are of funda- 
mental importance. Collected here are the available 
data on these materials. Clearly, the study of the 
reflection coefficients leads indirectly to the dielectric 
properties of these materials. Here we will be con- 
cerned more with the direct determination of their 
dielectric constants and loss factors. 

10.6.1 Experimental Methods 

R eflectiox-Teansmission Method 

First we should like to sketch here the basis of the 
different experimental methods used in the determina- 
tion of the dielectric properties of materials. 

One of these is the reflection-transmission method 
which was used by Ford^^ in his studies of the prop- 
erties of the ground. This same method has also been 
used recently by Saxton^®*®® on water in investigating 

®By L. Goldstein, Columbia University Wave Propagation 
Group. 


DIELECTRIC PROPERTIES OF WATER AND ATMOSPHERE 


181 


the temperature depejideiiee of its dielectric properties 
at 1.^5 and 1.58 cm. 

If the power transmitted through two thicknesses 
and of the material in question are 


Pi = Poe-“^i, 

P2 = Poe-^^2, 

then the absorption coefficient a is given by 

“ = Z T- logic — , (77) 

d'z — di 12 

where Pq is the incident power. 

The absorption index k in the complex refractive 
index 

N = 71 — jk (78) 

is related to the absorption coefficient by 

« = (79) 

A 

and hence 

fc logic (80) 

Txa P2 

where d stands for {d^ — d^). Also 

= {n — jky = €r — jei, 

= er- jQOaX. (81) 

cr is the real part of the dielectric constant, €» its 
imaginary part; cr is the conductivity of the sub- 
stance is mhos per meter; and A the wavelength in 
meters. One obtains readily from equation (81) 


n^-k^= er 

2nk = ei = 60o-X. 


(82) 


The absorption index k is measured directly by two 
galvanometer readings proportional to P^ and Pg. 
The refractive index n is derived from the reflection 
coefficient Hn for almost perpendicular incidence, 
using 


^^2 ^ n^ + k’^+l- 2n 
^ + 1 + 2n' 


(83) 


Then n and k determine €,. and o-. Saxton claims that 
in this method at least one quantity, the absorption 
index, is measured directly while the other, the re- 
fractive index, is derived from the measurement of 
the reflection coefficient. 

In the other methods, given later, neither of these 
quantities is measured directly. 


Standing Wave Ratio Method 

By limiting the electromagnetic field to the en- 
closure of a hollow pipe or coaxial line, the energy 
is completely confined, stray effects are eliminated, 
and small amounts of any dielectric can be inves- 
tigated accurately.^®"^^ The following gives the the- 
oretical foundation of this ‘^standing wave ratio” 
method for measuring complex dielectric constants. 

1. A transmitter radiates waves of a given fre- 
quency into one end of a closed wave guide. These 
are reflected by the metallic boundary at the other 
end. Standing waves are set up in the guide, and 
they can be measured by a probe detector traveling 
along a slot in the pipe parallel to its axis. The dielec- 
tric is inserted at the closed end of the pipe, opposite 
the transmitter, and fills the pipe up to a height d. 
Above it the standing wave pattern is measured in air. 
The real and imaginary parts e,- and ei of the dielec- 
tric constant are calculated from the ratio of the field 
strengths in node and antinode Emm/Pmax, and the 
distance Xq of the first node from the surface of the 
dielectric. 

The modulus and the argument of the reflection 
coefficient are obtained from 


R = p€-^‘^ = 


(Z(Q)/Zoi) - 1 
(Z(0)/Zoi) + l^ 


(84) 


where Z(0) is the characteristic impedance of the pipe 
section filled with the dielectric understudy, Zq^ is 
the intrinsic impedance of the air-filled portion of 
the pipe. By denoting 



= tanh 5 = tanh (5^ -\-j8i) , 


(85) 


where 8,. and 8i are, respectively, the real and im- 
aginary part of 8, the reflection coefficient R can be 
written as 


with 


R= \R\e-^'^, 
= pe-^^ , 


( 86 ) 


p = \R\ = e~^r'^Si,rg R — —TT — 25i = (87) 

From the expression of the reflected field strengths 
one finds that the distance Xq of the first node from 
the surface is given by 


Xo 



( 88 ) 


where 8i is connected directly to the phase shift at 
reflection through equation (87), and Ai is the wave- 


182 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


length in air of the radiation. The measurenient of 
Xq thus yields Bi. Similarly, one finds that 

tanh 8r = \ | • (89) 

2. Calculation of dielectric constant and loss fac- 
tor from terminating impedance. The intrinsic im- 
pedance of the dielectric-filled portion of the guide 
is found to be 

Z(0) = Zo2 tanh 72 d, (90) 

where 

(91) 

72 


Thk Uksoxatou Q METiioid^ 

Here the procedure consists in measuring the 
change of resonant frequency of a closed cylindrical 
resonator upon the insertion, along the axis, of a rod 
of the dielectric material in question. By observing 
the change of Q value resulting from the insertion of 
similarly dimensioned specimens of different mate- 
rials, it is possible to obtain comparative loss tangent 
values. The relevant theoretical relations are sum- 
marized below. 

By definition the Q value of a resonator system is 
given in convenient form by the relation 


The subscript 2 refers to the dielectric medium, 
is its permeability and 72 is the propagation constant 
of dielectric-filled section of the guide; for the TE 
waves, Zqo is the impedance of thg dielectric medium 
itself. Using equations (90) and (91), one gets 

tanh72(i ^ Ml ^g2) 

y2d Zoi dyi p2 


Q _ 2 ^ energy stored 

energy loss per half cycle 

Both the energy stored and the energy loss can be 
computed from the field distributions within the 
resonator, and these are given, for a TM wave, as 

He = AJi (7P), (98) 


The propagation constant y^ determines finally the 
complex dielectric constant €c through the funda- 
mental relation 


72 



1 



(93) 


where the cutoff wavelength Ac is determined by the 
geometry of the guide and the type of wave. In the 
air-filled section of the guide 

"'' = [(£)'■ "'"‘“I • 


Consequently, from equations (93) and (94), the 
complex dielectric constant of the material under 
study becomes 


(1/Xe)^- (72/27r)^ 

(1/X.)‘‘+(1/Xi)2 ’ 

where 


.27r 

for free space. Finally 



(95) 

(96) 

(97) 


The solution of equation (93) can be found from 
charts. It is claimed that with this method materials 
with very low dielectric losses can be investigated 
satisfactorily. 


E. p—Joiyf), ( 99 ) 

a + 

where is the tangential magnetic field strength 
in amperes per meter. E^ is the axial electric field 
strength in volts per meter, p is the distance of the 
point in question from the cylinder axis, 7 is the propa- 
gation constant 

7^ = /xerco^ — jcoo-p, 

0 ) is the angular frequency, p the permeability in 
henrys per meter, and ^4 is a constant determined by 
the strength of the exciting source. In the formulas 
(98) and (99) it was assumed that the walls of the 
resonator are of infinite conductivity so that no elec- 
tric intensity exists in them. This requires that 

Ez {p — a) = Jo (ya) = 0, (100) 

where a denotes the radius of the resonator. This 
equation has an infinite number of real roots, the low- 
est being ya = 2.4048, and this determines the fun- 
damental resonant frequency and wavelength Aq. If a, 
the conductivity of the dielectric, is neglected in com- 
parison with c^w, the propagation constant becomes 

7 = O) VM€r = — . (101) 

X 

cr is the dielectric constant of the material filling the 
resonator taken relative to air. Since A can be meas- 


DIELECTRIC PROPERTIES OF WATER AND ATMOSPHERE 


183 


iired, this dielectric constant may be derived from the 
relation 

= 2.4048 
X 
or 

No appreciable error will be committed in using the 
preceding results for the practical case of dielectrics 
with low but finite conductivity. 

The Q of the filled cylindrical resonator is shown 
to be 


tan 5 (103) 

Here d is the wave-guide skin depth, 2Zq is the axial 
length of the resonator and tan 8 = a/cr is the loss 
factor of the dielectric. Consequently 

where Qq is the Q of the air-filled resonator. 

It should he remembered in this connection that 
the theoretical Qq values, in general, are found to be 
considerably different from the measured ones. This 
tends to limit the reliability of the method. 

After having thus sketched the different methods 
used in the determination of the complex dielectric 
constant of substances of importance in wave propaga- 
tion, we turn now to the presentation of the data. 

Liquid Watee 

Table 17 gives the results obtained recently on 
liquid water.^^’^®'^®'^^ 


Table 17. Temperature variation of the dielectric 
properties of water. X = 1.24 cm.38,39 


t°C 

n 

k 

€r 

H 

(7 mhos/m 

0 

4.68 

2.73 

14.4 

25.5 

34.3 

3 



27* 

27* 

36.0* 

5 

5.24 

2.89 

19.1 

30.3 

40.7 

10 

5.74 

2.92 

24.4 

33.5 

45.0 

15 

6.17 

2.88 

29.8 

35.5 

47.8 

18 



32.T 

39.2^ 

51.8 

20 

6.53 

2.77 

34.9 

36.2 

48.6 

25 

6.84 

2.63 

35* 

23* 

30.6* 



.... 

39.8 

36.0 

51.1 

30 

7.10 

2.48 

44.2 

35.2 

50.0 

35 

7.30 

2.30 

48.0 

33.6 

45.1 

40 

7.47 

2.11 

51.3 

31.5 

42.4 

60 



44* 

14* 

18.6* 


*Data from reference 22, at X = 1.25 cm. 
^Data from reference 44, at ^ = 1.26 cm. 


It has been found by Saxton and Lane that the 
temperature variation of the dielectric constant in the 
range 0 to 40 C at 1.24 and 1.58 cm can be ac- 
counted for with simple theoretical formulas. At any 
given temperature one single characteristic constant, 
the ^Telaxation time,’^ was' sufficient to account for the 
frequency dependence of the complex dielectric con- 
stant of water.' The formulas in question are the 
following : 


or 


and 

Here 



is + 

€s + €oX^ 


€s + €sX^ 

1 ' 


€i = 2nk. 

X = COT = 27r/r, 


(105) 


(106) 


with T denoting the relaxation time, is the static 
dielectric constant, co the optical dielectric constant 
due to the sum of the electronic and atomic polariza- 
tions. 


Table 18. Temiierature variation of the dielectric 
properties of water. 38, 39 x = 1.58 cm. 


ec 

n 

k 

Cr 

H 

d mhos/m 

0 

5.24 

2.90 

19.0 

30.4 

32.0 

5 

5.84 

2.97 

25.3 

34.7 

36.6 

10 

6.36 

2.91 

32.0 

37.1 

39.2 

15 

6.77 

2.78 

38.1 

37.6 

39.7 

20 

7.13 

2.61 

44.0 

37.2 

39.2 

25 

7.40 

2.41 

49.0 

35.7 

37.6 

30 

7.59 

2.21 

52.7 

33.5 

35.4 

35 

7.72 

2.01 

55.5 

31.0 

32.7 

40 

7.81 

1.80 

57.7 

28.1 

29.7 


Considering t as a parameter to be derived from 
the experimental data, one finds in Table 19 the re- 
laxation times in the 0 to 40 C temperature range. 


Table 19. Relaxation times of water at different tem- 
peratures.38,39 


ec 

r X 10^2 sec 

ec 

T X 10^2 sec 

0 

19.0 

25 

6.8 

5 

14.6 

30 

5.9 

10 

11.85 

35 

5.2 

15 

9.6 

40 

4.5 

20 

8.1 




184 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 




Table 20. Temperature variation of the dielectric properties of water.45,<<5 

X = 10 

cm. 




Refractive index n 


Absorption index k 

er calc 

€,• calc 

(T mhos/m 

Calc 

Experimental 

Calc 

Experimental 

X = 9.72 cm 

X = 10 cm 

X = 9.72 cm 

X = 10 cm 

0 

8.99 

8.95 


1.47 

1.35 


78.66 

26.43 

4.40 

5 

9.04 



1.14 



80.42 

20.61 

3.44 

10 

9.02 

9.00 


0.90 

1.10 


80.55 

16.23 

2.70 

15 

8.96 



0.76 



79.7 

13.61 

2.27 

20 

8.88 

8.88 

8.84 

0.63 

0.90 

0.66 

78.46 

11.20 

1.84 

25 

8.80 



0.50 



77.20 

8.80 

1.46 

30 

8.71 

8.75 

8.69 

0.45 

0.73 

6.54 

75.66 

7.84 

1.30 

35 

8.62 

.... 


0.40 



74.14 

6.89 

1.16 

40 

8.53 

8.60 

8.56 

0.36 

0.60 

0.40 

72.63 

6.15 

1.02 


Table 20 refers to 10-cm waves for which measure- 
ments were made in the temperature range 0 to 
40 In one series of measurements the wave- 

length was 9.72 cm, but this is considered close 
enough to have the corresponding data included with 
the 10-cm waves. 

The preceding table indicates that the agreement 
between calculated and measured values of n and Ic 
is satisfactory. It is to be noted here that the experi- 
mental results on S band were obtained by the stand- 
ing wave ratio method, those at K band with the reflec- 
tion-transmission method. 

Using equations (105) and (106), the temperature 
variation of the refractive and absorption index, or 
real and imaginary parts of the complex dielectric con- 
stant, can be computed at any wavelength provided 
that the relaxation time at the temperature in ques- 
tion is known. 

In Tables 21 and 22, the temperature variation of 
the indices n and Ic are given. These results were com- 
puted with the aid of formulas (105) and (106). 

It is thought^®’^® that until more extensive experi- 
mental results become available the computed values 
can be regarded as representing the best information 
available on the dielectric constant of water in the 
millimeter and centimeter range. Figure 25 represents 
the best available information on water at 20 C. 


Table 21. Temperature variation of the dielectric 
properties of water.38,39 x = 0.50 cm. 


ec 

n 

k 

€r 

ei 

a mhos/m 

0 

3.18 

1.76 

7.01 

11.2 

37.3 

5 

3.50 

2.03 

8.13 

14.2 

47.3 

10 

3.80 

2.25 

9.38 

17.1 

57.0 

15 

4.10 

2.41 

11.0 

19.7 

65.6 

20 

4.39 

2.54 

12.8 

22.3 

74.3 

25 

4.67 

2.62 

14.9 

24.4 

81.3 

30 

4.94 

2.67 

17.3 

26.4 

88.0 

35 

5.21 

2.69 

19.9 

28.0 

93.3 

40 

5.47 

2.69 

22.7 

29.4 

98.0 



Figure 25. Refraction and absorption indices for 
water. 


Ice 

A certain number of measurements on the dielectric 
constants of ice were made in the centimeter wave- 
length range. The British workers^^ used the resonator 
Q method at 3 and 9 cm. The latest results on both 
these wavelengths are collected on the accompanying 
graph (Figure 26). The temperature range extends 
from about — 50 C to 0 C. The refractive index turns 
out to be constant in this range. It was found to be 
equal to 1.75 at 3.01 cm and 1.72 at 9.18 cm. The 
absorption index increased in this temperature range 
from about 0.0001 to 0.0010. 


Table 22. Temperature variation of n, k, and <r.38,39 
X = 3.2 cm. 


t°C 

n 

k 

Cr 

€i 

0 - mhos/m 

0 

7.10 

2.89 

42.0 

41.1 

21.4 

5 

7.63 

2.62 

51.3 

40.0 

20.8 

10 

8.00 

2.33 

58.6 

37.3 

19.4 

15 

8.22 

2.00 

63.6 

32.9 

17.1 

20 

8.33 

1.72 

66.4 

28.7 

14.9 

25 

8.38 

1.50 

68.0 

25.1 

13.1 

30 

8.39 

1.31 

68.7 

22.0 

11.4 

35 

8.38 

1.16 

68.9 

19.4 

10.1 

40 

8.35 

1.02 

68.7 

17.0 

8.85 


LABORATORY MEASUREMENTS OF DIELECTRIC PROPERTIES 


185 



Figure 26. Absorption index {kxlO+^) versus tem- 
perature for ice. 


Y^ounker,^^ using the standing wave ratio method 
at 1.25 cm, found at about — 15 C 

c,- = 3.3 and ei = 0.011, or o- = 0.013 mhos/m. 

These data can be compared with those obtained at 
3.01 cm,^^ where 

€r — 3.06 and ei = 0.00080, o- — 0.00044 mhos/m. 

The difference at these two wavelengths between the 
conductivities appears much too large and further 
studies should clear up this discrepancy. The dielectric 
losses in ice in the centimeter region are, however, 
\cry small. 

At much lower frequencies the dielectric behavior 
of ice is given in Figure 27. These data refer to a 
temperature of — 12 

Attenuation Due to Water Vapor 

In order to determine the attenuation due to water 
vapor, Saxton endeavored to measure the refractive 
and absorption indices of water vapor Using the 
resonator Q method, he found that by passing from 
9 to 3.2 cm the real part of the dielectric constant 
changes from 1.0056 to 1.0051. According to a general 
relationship connecting the real and imaginary parts 
of the complex dielectric constant,^® the indicated 
variation of — 1) given by Saxton should be accom- 
panied by a tremendous absorption by water vapor in 
the microwave region as pointed out by Van Vleck.^^ 
This is contrary to the data available and rules out 
the frequency variation of — 1) given by Saxton. 



Figure 27. Loss factor and dielectric constant of ice. 

According to Van Vleck, in the microwave region out- 
side of any resonance region, the ref raction [ ( — 1), 
n being the refractive index] or {er — 1), must be 
appreciably constant over the microwave region to 
account for the absence of any large absorption co- 
efficients. 

The conclusion is similar in case of resonance 
which occurs for both O 2 (0.25 cm and the 0.5-cm. 
band) and HgO (^1.30 cm). The refractive index of 
the atmosphere free of condensation should be con- 
stant throughout the microwave region. The refrac- 
tive index for infinitely long waves or the static dielec- 
tric constant can be used here. In the presence of con- 
densation, clouds, fog, and rain, the attenuation is 
increased considerably, and the refraction or (e,. — 1) 
might then differ from the static value. But under 
standard conditions, the refraction of the atmosphere 
should not change by more than a few parts in a 
thousand in the microwave region. 

^ LABORATORY MEASUREMENTS OF 
DIELECTRIC PROPERTIES'^ 

The working committee of Ultra Short Wave Panel 
has presented a report dealing with the measurement 
in the laboratory of 

1. The dielectric constant and loss angle in super- 
heated steam for wavelengths in the S, X, and K 
bands. 

*By F. Hoyle, Ultra Short Wave Panel, Ministry of Supply, 
England. 


186 


DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 


2. The dielectric constant and conductivity of bulk 
water for the K band. 

These experiments have been carried out by Saxton. 
The method adopted on S and X bands in (1) was to 
allow superheated steam to isue freely through a 
resonator into the air. The pressure throughout the 
apparatus was accordingly the atmospheric pressure. 
The temperature of the steam was measured before 
entering and after leaving the resonator. The temper- 
ature difference between these measurements was no 
more than 2 C, so it seems clear that no condensation 
of water droplets could occur within the resonator. 
A somewhat different technique was employed for 
X band in that the resonator was replaced by a wave 
guide. If c is the dielectric constant, then the best 
representation of the results is obtained by plotting 
(c — 1) against l/T, for each wavelength where T 
is in degrees absolute. It was found that the results 
for different values of T fitted very well to a straight 
line as they should theoretically, but the value of 
(c — 1) for all values of T was found to be systemati- 
cally about 10 per cent less than would have been 
expected on the basis of previous measurements of the 
dielectric constant of steam at much longer wave- 


lengths. This discrepancy was found on X and K 
bands. The reason for the discrepancy is not yet under- 
stood. It is known, however, that the reduced value of 
(c — 1) does not arise from strong dispersion occur- 
ring in the microwave band since there is no evidence 
of any abnormal absorption. 

The method adopted in (2) was to measure first the 
attenuation factor of radiation passing through water. 
This was done by placing a transmitting horn above 
a large shallow trough and a receiving horn below 
the trough. The attenuation factor was measured im- 
mediately by varying the depth of the water in the 
trough. Second, the reflection coefficient of electromag- 
netic waves incident normally on a plane surface of 
water was measured. These two observations were 
sufficient to determine the dielectric constant and 
conductivity of water. The results obtained for a 
wavelength of 1.58 cm were: 

Dielectric constant about 40; 

Conductivity about 4.10 esu.^^ 

The same values were obtained for both tap water and 
distilled water, showing that the presence of salts in 
the water had little effect on the value of the con- 
ductivity. 


Chapter 11 

STORM DETECTION 


1 STORM DETECTION BY RADARS 

T his summer (1944) a study was made of the 
meteorological echoes observed on a Canadian 
microwave S-band early warning radar set at Ottawa. 
These were correlated with check observations on the 
weather made by a large number of local observers dis- 
tributed over the area covered by the set. It was found 
that observers inside the source area of the echo always 
reported rain; just outside the echo (1 to 5 miles) 
there was a half chance of light rain. Atmospheric 
electrical disturbance was present in less than half 
the cases checked. Echoes became less frequent at in- 
creasing distances from the set but in some cases were 
seen at 160 miles. 

The display system that we have used is a plan posi- 
tion indicator [PPI] tube. This tube provides a map 
of a circular area centered on the location of the set 
and extending out at choice to 40 or 80 or 160 miles. 
The last-mentioned setting was the one used most of 
the time. 

Procedure 

During the hours of operation a 16-mm motion- 
picture camera was kept running, taking pictures of 
the PPI display and a clock alongside, exposing one 
frame of the film for the duration of each revolution 
of the array. Thus about four photographs were ob- 
tained per minute. At the same time we watched the 
progress of moving echoes across the screen and made 
telephone calls to any observers that were available, in 
the neighborhood of any echo. From the observer the 
existing state of the weather was determined; his re- 
marks and the exact time were carefully noted. 

We checked the echoes and their movement as re- 
corded on the film against the information obtained 
about the weather from the observers. We also made 
charts of the echoes, based on the film, at 30-minute 
intervals. 

11.1.2 Weather Information 

Facilities of which we availed ourselves for obtain- 
ing information were, among others : 

• By Col. J. T. Wilson, Director of Operational Research, 
NDHQ, Canada. 


1. Ottawa meteorologi^-al stations. These stations 
provided us with as many as three forecasts a day and 
with weather information generally. 

2. Distant meteorological stations. Apart from the 
Ottawa stations, the nearest weather station, 57 miles 
away, is at Canton, N. Y. Its reports are included in 
the teletype sequences that come to us. 

3. Unofficial observers, consulted by telephone. Since 
the official weather stations did not provide the close 
network that we required, we compiled a list of per- 
sons whose location could be closely marked on our 
map and whom we could consult about existing 
weather conditions to the extent that an untrained 
observer would be competent. 

Correlations 

Our aim was to correlate observed echoes with 
weather conditions. At first clouds were thought to be 
possible sources of echoes, and it was thought that 
fronts might produce some sort of echo quite inde- 
pendently of cloud or precipitation along the front. 
The earlier part of our work showed that on after- 
noons with heavy cumulus clouds but with no pre- 
cipitation there were no weather echoes. On days with 
scattered showers, however, echoes were observed. 
Also, the passage of a front did not seem to produce 
any peculiar sort of echo or any echo that could not 
be attributed to precipitation along the front. 

In analyzing our correlations, we have found it 
convenient to consider them in two groups. First, there 
are correlations with echo, that is, correlations when 
the observer was in the vicinity of an echo, although 
not necessarily right inside the echo. All correlations 
involving telephone calls to local observers were of 
this type, for we didffit make such a telephone call 
unless there was an echo in the vicinity. Second, there 
are correlations with weather, or correlations with 
weather stations, when we first select an occasion wlien 
precipitation is reported (by an official station) and 
then go looking in our records for an echo to match. 
Nearly all the precipitation recorded at the weather 
station during our hours of operation was light, and 
too light, as it proved, for us to detect it at the distance 
we were away. Thus there is only a very small number 
of echoes associated with correlation with weather. 


187 


188 


STORM DETECTION 


and so very little overlapping between this group and 
the group of correlations with eclio. 

Correlations with Echo 

Table 1 gives a summary of the results obtained in 
the form of a comparison of precipitation observed in- 
side and just outside the echoes. 

Table 1. Precipitation inside and just outside echoes. 

Observer’s position relative to echo 


Inside Outside 



No. 

% 

(1 to 5 miles) 
No. % 

Cases of no rain 

0 

0 

19 

48 

Very light rain 

6 

13 

7 

17 

Light rain 

16 

33 

13 

33 

Moderate rain 

13 

27 

1 

2 

Heavy rain 

13 

27 

0 

0 

Total 

48 

100 

40 

100 


11.1.5 Correlations with Weather Stations 

Correlations with weather stations were notable 
chiefly for the rain we did not detect. Nearly all the 
precipitation observed at the station was light and 
apparently too light to produce echoes effective at such 
distances. Weather reports on the teletype from Ot- 
tawa itself were not correlated with echoes because 
most meteorological echoes within 10 miles were ob- 
scured by permanent echoes and distortion at the 
center of the PPT. The next closest weather station is 
at Canton, N. Y., 57 miles from our set. The rainfall 
for every hour was obtained from a rain gauge at 
Canton, and in addition some of the teletyped weather 
reports were received. Pain was reported from Canton 
on five occasions during our hours of operations. On 
one of these occasions we had an echo directly over 
Canton ; on three others we had an echo within three 
miles of Canton ; on one occasion we had no echo in the 
vicinity at all. The details are given in the table. It can 
be seen that we detected rain falling at a rate of 0.2 in. 
per hour and failed to detect rain falling at a rate of 
0.03 in. per hour. 


Table 2. Rain at Canton, New York (U. S. Weather 
Station, 57 miles from set) during analyzed hours of 
operation. 


Case 

Rainfall 
in. /hr* 

Thunder 

Echo 

1 

0.20 

Yes 

Overhead 

2 

0.05 

Yes 

1 mile away 

3 

0.3 

Yes 

2 miles away 

4 

Trace 

No 

3 miles away 

5 

0.03 

Yes 

No echo 


♦All rates taken from gauge reading made at hourly intervals. 


11 . 1.6 Resume of Correlations 

Our checks with local observers out to 60 miles 
from the set revealed the following: Inside the echo 
there is sure to be rain, with a 0.3 chance that it is 
moderate or heavy. Just outside (1 to 5 miles) there 
is never more than light rain, and a half chance of 
none at all. Further, the chance of an observer in the 
vicinity of an echo reporting thunder was 0.4. Our 
checks with weather stations were less relevant, be- 
cause only two echoes passed over weather stations 
during the period studied. But from the numerous 
cases of light rain at these stations that we did not 
detect, we can say that we cannot detect light rain at 
90 miles. By light rain we mean rainfall less than 0.1 
in. per hour, and this can just be detected at 50 miles. 
Further, to judge by one storm that we detected and 
one we missed at Canton, we can detect 0.2 in. per 
hour and cannot detect 0.03 in. per hour at 57 miles. 

Fraction Detected by Radar of 
Total Quantity of Rainfall 

Starting from the proportion of hours of rain that 
give an echo, we have used the distribution with rate 
of rainfall of the hours of rain to give us a value for 
the minimum rate of rainfall that will give us an 
echo. Now using a distribution witli rate of rain- 
fall of the quantity of rainfall, we can proceed to de- 
termine the proportion of the total quantity of rain 
that was observed by radar. The proportion is quite 
high : 83 per cent close to the set, 62 per cent at 
50 miles. 

11 . 1.8 Comparison with Ryde’s Theory 

Computations of the echo strength to he expected 
have been made on the basis of the theory developed 
by J. G. Pyde of the General Electric Company (Brit- 
ish). The experimental results are in satisfactory 
agreement with theory. (See Section 10.1.) 

11.1.9 rpjjg Best Frequency for Storm 

Detection 

The sensitivity to rain of the frequencies we have 
been using is such that with the power available we 
can obtain satisfactory performance. At higher fre- 
quencies the sensitivity, according to theory, is con- 
siderably higher, but considerations of absorption 
made by Ryde would keep us from going to much 
higher frequencies. Absorption affects us in two dif- 
ferent ways. In the case of widespread rain, even of 
moderate intensity, there is enough absorption between 


S-BAND RADAR ECHOES FROM SNOW 


189 


the set and the echo source to reduce our effective range 
cousiderabl 3 \ \Miere there is no widespread rain but 
the rain that we want to see is heavy and concentrated, 
the absorption of high-frequency radiation by heavy 
rain can be so great that hardly any of the radiation 
impinging on the storm makes its way back out to be 
reflected. We could actually fail to detect a storm in 
this way, because the storm was too intense. The fre- 
quency we are using ( S-band) is safe against both these 
effects, but increasing it by a factor 3 would lead us well 
into them. 

11.1.10 Range— Greater Range 

of a Production Set 

The performance of the prototype set we have used 
has been specified in the previous section by its range 
for aircraft. The performance of the same design of 
set, constructed and installed to the final production 
specification, is known to be better : the range for air- 
craft is approximately twice as great, and some calcula- 
tions show that very roughly the range of a produc- 


tion set for storms will be twice that of our proto- 
type set. 

The full account of this work is published as: Sum- 
mer Storm Echoes on Radar MEW, Report No. 18 
of the Canadian Army Operational Research Group; 
27 Nov., 1941. 

“ 2 S-BAND RADAR ECHOES FROM SNOW‘D 

Since June 1944^ the Canadian Army Operational 
Research Group has been studying the nature and ap- 
plication of S-hand radar echoes from storms. During 
the past winter we studied echoes from snow, obtained 
on occasions when snow was present and rain definitely 
was not. 

Heavy snow has been detected on five occasions, 
with maximum ranges varying from 30 to 65 miles. 
One moderate snowfall which kept all aircraft 

^By J. S. IMarshall, Canadian Army Operational Research 
Group. 



Figure 1 . Typical S-band PPI display of snow echoes. 



190 


STORM DETECTION 


grounded was not detected at all, even at the minimum 
range of 10 miles. 

Eoughly, rain and snow of the same intensity, ex- 
pressed in inches of liquid water per hour, produce 
about the same echo and are detectable to the same 
range. Further, there seems to be no useful difference 
in pattern between echoes from the two sources. Fig- 
ure 1 shows a typical PPI picture of snow echoes made 
during the course of the study. 

Theoretically, this equality is not directly signifi- 
cant ; in the case of snow there is a much greater bulk 
of lighter material, falling more slowly and reflecting 
less well. 

Operationally, there are two reasons why radar 
storm detection is less useful in winter (in Canada). 
A given intensity of precipitation in the form of snow, 
say 0.1 in. of water per hour, is much more hazardous 
to flying and to ground activities than the same inten- 
sity in the form of rain. Further, great intensities of 
precipitation such as lead to long-range echoes in 


summer are almost nonexistent in winter in this 
region; therefore, detection at great ranges is not 
achieved. Thus S-band radar in summer can detect 
important storm areas to a radius of about 100 miles; 
in winter it detects hardly any weather beyond 50 
miles and misses some important snow even at 10 to 20 
miles. 

For the greatest total contribution of radar to fly- 
ing it is a good thing that echoes from snow are weak. 
This is important, for while the cumulo-nimbus ac- 
tivity detected in summer must always be avoided by 
aircraft because of violent air currents, flying in mod- 
erate snow can be safe with good blind-flying control. 
It is fortunate, therefore, that echoes from snow are 
probably not strong enough to interfere with any radar 
elements of this control. 

This work has been done with the cooperation of 
the National Research Council of Canada, the Ca- 
nadian Meteorological Service, and the Royal Canadian 
Air Force. 


Chapter 12 

ECHOES AND TARGETS 


12 1 FLUCTUATIONS OF RADAR ECHOES" 

S INCE JUNE, 1943, the Propagation Group of the 
Radiation Laboratory has had a project under way 
to investigate the nature and origin of fluctuations 
from close targets. This work has been done in the 
microwave region using the mobile S- and X-band 
sets belonging to the group. Most of the work has been 
on S band. AVe have restricted ourselves to targets 
sufficiently close to the radar that the more usual 
effects of atmospheric refraction can be neglected. 
AA"e have not paid much attention to moving targets 
such as ships or planes, as their echoes are easily ac- 
counted for by the changing aspect of the target, 
propeller modulation, etc. 

One of the obvious sources of signal fluctuation is 
instability in the system. In our case system instabil- 
ity was chiefly due to ripple in the receiver, and sen- 
sitivity to changes in line voltage affecting the modu- 
lator, receiver, and indicator units. After considerable 
effort these forms of instability have been reduced but 
not completely eliminated. The transmitted pulse 
shows an average fluctuation about the mean of ±0.1 
db with a maximum deviation about 0.5 db. Pulse-to- 
pulse frequency changes are not greater than 0.1 or 
0.2 me, and frequency modulation inside the pulse is 
less than 0.2 to 0.3 me. These flgures are for the S- 
band set, and instability is somewhat greater on X. 
The r-f signal intensity is measured by comparison 
with a pulse from a calibrated signal generator. This 
pulse shows a fluctuation as large as the transmitted 
pulse, i.e., about ±0.12 db. It is believed that this 
apparent change is not in the signal generator but 
rather in the receiver and indicator units. 

Some radar signals show almost as little fluctuation. 
These are large man-made targets in isolated posi- 
tions viewed over land. Some examples that we have 
found are the Provincetown standpipe as viewed from 
Race Point in Provincetown and the Winthrop stand- 
pipe in Boston viewed from Deer Island. In these 
cases the average pulse to pulse deviation from the 
mean is ±0.14 db. Such steady signals are the rare 
exception. Most echoes show changes that are much 
larger than can be accounted for by instability in the 
system tests. 

*By H. Goldstein, Radiation Laboratory, MIT. 


12.1.1 Interference Concept 

When this research was started, it seemed to be a 
common idea that changes in atmospheric refraction 
in the path between the target and set could account 
for the observed variations. We have found little evi- 
dence for this belief. If the targets are closer than 10 
miles, the effects due to the atmosphere, if there are 
any, must be small compared to the more important 
phenomena shown by the echoes. The behavior of the 
radar echo is determined by the fact that a radar signal 
is usually not the return from a single target but rather 
the sum of returns from all targets within the area 
illuminated by the set. Since the radar beam is co- 
herent, the individual signals must be added in am- 
plitude taking into account the relative phase of the 
echoes. The total signal is the result of the interference 
between these component echoes. In the case of the 
standpipes mentioned above there were intervening 
hills so that only the top portions of the targets were 
seen by the radar, but in most other cases there is 
more than one target present, and the interference 
between these targets will determine the nature of 
the total echo. 

In the Boston region, we have found one very simple 
dual target consisting of two radio towers 500 ft high 
and 60 yd apart in range. Both constructive and de- 
structive interference has been observed in this case. 

The changes in the phase between the component 
signals might be due to several causes. If the index of 
refraction in the path between the two towers changes, 
then the optical path length would change. However, 
the deviation of the index from 1 would have to double 
in order to produce sufficient phase change. A change 
in the frequency of the transmitter could also account 
for the phase change. To produce the observed effect 
it would have to be greater than V 2 me, which is larger 
than the frequency instability of the system. Finally, 
the towers themselves could physically move relative to 
each other and produce the phase change in a manner 
similar to that in the Michelson interferometer. To 
produce a phase change of tt the targets need only move 
A/4 relative to each other. At S band this amounts to 
1 in. It does not seem unnatural that such tall struc- 
tures might sway in the wind by even a greater amount. 
To test this conclusion the signal from these towers 


191 


192 


ECHOES AND TARGETS 


was measured over a period of 4 days. The amount of 
fluctuation was estimated visually every half hour. 
These results showed a definite correlation with the 
speed of the wind. Large fluctuations occurred only 
with high winds. It was calculated that if the fluctua- 
tion had indeed been independent of wind speed the 
odds against getting the set of readings obtained by 
these measurements would be 10,000,000 to 1. 

12.1.2 Assemblies of Random Scatterers 

In a more common type of radar target the entire 
illuminated area contains a large number of independ- 
ent targets with random phases. If we represent the 
signal from each target by a vector showing amplitudes 
and phase, then the total signal is found by adding 
up all these vectors. If the phase of the individual 
vector is changed slightly (for instance, by relative 
motion) this vector diagram would be rearranged and 
the total signal changed. Some practical examples are 
precipitation echoes, where the individual targets are 
the drops; window, where the echo arises from many 
strips of tin foil; and sea echo, where the individual 
targets are probably areas of reflection from the sur- 
face of the sea. 

The theory of this type of target has been extensively 
worked out.^"^ One of the questions that can be an- 
swered by the theory is to determine the probability 
P(7) that a given signal from the target will be of 
intensity I in range dl. Or equivalently, one can find 
the fraction of returned pulses having intensity I in 
range dl. [P(/) has been called the first probability 
distribution.] The result is simply 

P(I)dI = 

10 

where Iq is the average intensity of the echo. The con- 
tinuous curve in Figure 1 is a plot of this experi- 
mental formula. 

The equation for P(I) is independent of the dis- 
tribution of the individual amplitudes, nor is it re- 
quired that the individual amplitudes be constant 
with time, only that the distribution shall be station- 
ary with time. The only other conditions that must be 
satisfied are that there shall be a large number of scat- 
terers and that they shall be independent of each other 
with phase random both in space and time. It will be 
seen from the formula that the most probable signal is 
always zero. Furthermore the distribution is indepen- 
dent of the number of targets. The rapidity of the fluc- 
tuations is determined essentially by the echo changes 


and the relative velocity of the scatterers. The detailed 
relation has been worked out between the frequency 
spectrum of the fluctuations and the velocity distribu- 
tion of the particles.® The frequency of fluctuations 
should increase linearly with r-f frequency. 

In order to investigate experimentally this type of 
radar signal, it is necessary to get some method of 
measuring the intensity of the individual pulses. In 
our case this was obtained by photography of the single 
sweeps on the A scope. For this purpose a special A 
scope was used with a blue screen tube operated at 6 
kv. Commercial 16-mm movie cameras were used in 
which the shutter and claw had been removed and to 
which a high-speed motor drive had been added. 

By photographing a calibrated r-f signal generator 
pulse at the same receiver gain but at different r-f 
levels, one can obtain a curve for the deflection in 
centimeters against r-f intensity. By means of this 
curve the measured deflections from the pulse-to-pulse 
films can be converted into measurements of r-f in- 
tensity. From these expeirimental data it is possible 
to compute an experimental first probability distribu- 
tion. 

Figure 1 is an example of such an experimental dis- 
tribution obtained by measuring a thousand pulses of 



Figure 1. The first probability distribution, P (I) of 
the intensity of cloud echoes. Curve: P(/)=e"^/^o 
Histogram: experimental results. Film 90, S band, 
1,000 pulses. 

precipitation echo on S band. The continuous curve in 
that figure shows the theoretical formula given above. 
The agreement is good. 

By what is essentially a Fourier analysis of these 
data, one can also determine the frequency spectrum 
of the video signal. Figure 2 shows such an experi- 
mentally determined frequency spectrum for sea echo 
on both S and X bands. The spectrum extends to 
120 c on X band and about 50 c on S. The ratio be- 


FLUCTUATIONS OF RADAR ECHOES 


193 



V IN CYCLES PER SECOND 

Figure 2. Experimentally determined frequency spec- 
trum for sea echo. 


tween the width of the spectra is 2.4 compared to 
2.88 for the ratio of wavelengths. This discrepancy is 
probably due to the crudity of the measurements on 
X band. 

Ground Clutter 

The ordmary ground clutter consists of echoes from 
a variety of types of targets-: earth, rocks, trees, 
branches, bushes, leaves, grass. Our present conception 
is that the fluctuation in ordinary ground clutter arises 
from the motion of leaves and branches in the wind, 
changing the phase patterns in a manner somewhat 
similar to that for random scatterers. There will in 
addition be a relatively steady signal from fixed ob- 
jects such as rocks and tree trunks. 

\Ye have obtained much qualitative evidence for 
this picture, but it is difficult to obtain quantitative 



WIND SPEED IN MPH — » 

Figure 3. Fluctuation in signal from Blue Hills versus 
wind speed. S band, 10 a.m. April 24, 1944 to 11 a.m. 
April 25, 1944. 



Figure 4. First probability distribution. Baker Hill, 
Maine. Wind speed 25 mph. Curve: theoretical, fixed 
to random signal =1 db. /o = average intensity. 
Histogram: experimental results. Film 103, 3,000 
pulses, S band. 

data because the wind speed at the target is not usually 
known. Fortunately, in the Boston area the largest 
ground signal is due to the Great Blue Hills, which 
is the site of the Blue Hill Observatory. It is thus 
possible to obtain data on the wind speed at the target. 
We monitored the signal from Blue Hills for a 24-hr 
period in April of 1944. Movies were taken of the 
A scope at regular intervals. During the period of 
observation the wind speed varied between 30 mph 
and dead calm. To interpret the data a somewhat crude 
parameter was defined as a measure of the amount of 
fluctuation. The change in the signal strength from 
one frame to the next (0.06 sec) was measured and 
averaged over 200 frames. 



Figure 5. First probability distribution, Mt. Penobscot, 
Maine. Wind speed 10 mph. Curve: theoretical, fixed 
to random signal = -|- 7.2 db. /o = average intensity. 
Histogram: experimental results. Film 82 (16 fr per sec), 
400 frames, S band. 


194 


ECHOES AND TARGETS 



This parameter was then plotted against the wind 
speed as shown in Figure 3. There is a quite good 
correlation between the amount of fluctuation as meas- 
ured by this parameter and the speed of the wind. The 
fluctuation is of the order of 0.2 db at 0 mph, which 
is almost as good as our steadiest signals. At the other 
extreme the fluctuation is about 3.4 db at 30 mph. 
There appears to be a rather sudden jump in the fluc- 
tuation at a wind speed in the neighborhood of 20 
ni])h. This jump has been observed at other seasons of 
the year and is believed to be rather general. It is sig- 
nificant that the wind speed at which the jump occurs is 
roughly that at which large branches and small trees 
begin to move as a whole. 

The theoretical description for a simple picture of 
ground clutter consisting of an assembly of random 
scatterers (leaves, grass, etc.) plus a fixed signal 
(rocks, trees, trunks) is not difficult to work out. When 
the proportion of steady signal is small, the first prob- 
ability distribution closely resembles that for purely 
random scatterers. For a large ratio of fixed-to- 
random signal the amount of fluctuation is greatly 
reduced, and the first probability distribution tends 
to a Gaussian curve about the average intensity. This 
is illustrated in Figures 4 and 5. Figure 4 is a plot of 
the experimentally determined first probability dis- 
tribution for a signal from heavily wooded terrain on 
S band at 25-mph wind speed. This has been fitted 
by a theoretical curve for a ratio of fixed to random 


signal of — 0.1 db. 

Figure 5 shows the distribution for a similar type 
of terrain but for a wind speed of 10 mph. Here the 
results are fitted to a curve for a ratio of fixed to 
random signal of -|- 5 db. The most probable intensity 
is no longer at zero, and the amount of fluctuation is 
considerably reduced. 

Figure 6 is a plot of the intensity of some ground 
clutter at high wind over a period of It^ seconds as 
obtained from a pulse-to-25ulse film. While the signal 
changes quite rapidly, it is not nearly so fast as sea 
return, for examjfie (see Figure 7). 



Figure 7. Video frequency spectrum for ground clutter, 
Baker Hill, Maine. Film 103, wind speed 25 mph, prf 
333 M per sec, wavelength S band. 


THE FREQUENCY DEPENDENCE OF SEA ECHO 


195 


The frequency spectrum can be obtained from these 
data as in the previous case. Figure 7 shows the video 
frequency spectrum obtained under the same condi- 
tions as Figure 4 for high winds. The spectrum ex- 
tends as high as 12 c. Figure 8 is a plot of the fre- 



Figure 8. Video frequency spectrum for ground clutter. 
Mt. Penobscot, Mt. Desert Island. Film 82, wind 
speed 10 mph, wavelength S band, prf 333 K. 


quency spectrum obtained from the same film as in 
Figure 5. Here at a wind speed of 10 mph the fre- 
quency spectrum does not extend beyond 2 c. 

12.1.4 Targets Viewed over Water 

In addition to the sources of fluctuation described 
above, echoes from targets viewed over water will 
change due to the varying reflection from the surface 
of the sea. Some English investigations have shown 
that at high angles of incidence the amount of reflec- 
tion can often change quite rapidly. However, there 
is another effect due to reflection from the sea surface 
which is of a much longer period, namely, tidal varia- 
tions. 

Some of our earliest work consisted of monitoring 
the signal from a number of isolated targets viewed 
over water over a period of many tidal cycles. It was 
found that quite a large number of echoes showed a 
definite correlation with the tide. One very striking 
example is the case of two standpipes on Strawberry 
Hill on Nantasket Peninsula, which when viewed 
from Deer Island in Boston Harbor showed a 15-db 
variation with tide. Their range is 10,000 yd, and the 
targets are about 60 ft high. Under these conditions 


the targets subtend more than two lobes of the inter- 
ference pattern at S band. Since the effect of the tidal 
change is to move this lobe structure up and down by 
10 ft, it is difficult to believe that a change as large as 
15 db could be thus produped. However, one can break 
up the returned signal into a number of separate sig- 
nals differing as to whether they suffer two reflections 
on the surface of the sea or one reflection or go directly 
to and from the target. While the amplitude of each 
of these signals does not vary much with tide, their 
relative phases do, and the total signal can still change 
considerably in amplitude because of the interference. 
A similar set of measurements was made on a corner 
reflector mounted on a small island in Boston Harbor. 
Here the corner reflector although only 6,000 yd away 
acts essentially as a point target. The agreement with 
the theory for a point target is quite good. 

Our results emphasize the extreme caution that must 
be employed in the use of standard targets to monitor 
radar performance. They are just the type of targets 
which are normally chosen in the field, and obviously 
their variations with the tide make them entirely un- 
suitable for the purpose. It may be possible to find tar- 
gets whose echoes are sufficiently steady so that they 
can be used for monitoring. However, they cannot be 
found without the use of such test equipment as would 
obviate the need for standard targets. 

12.2 the FREQUENCY DEPENDENCE 
OF SEA ECHO^ 

As the power and frequency of radar sets continue 
to increase, and the size of the target to be detected 
decreases, the presence of sea echo becomes of ever 
greater operational significance. It acts as a built-in 
jammer, blanketing and obscuring the desired signals. 
Despite this growing practical importance the basic 
phenomena of sea echo have not yet been established. 
Certainly, the fundamental mechanism responsible 
for the signal is not yet known. Various conflicting 
theories have been proposed. It has been suggested 
that scattering from drops of spray is the cause of 
the echo. Another hypothesis is that of reflection or 
diffraction from the large surfaces of the waves them- 
selves. Still other theories have been advanced at one 
time or another. 

Whatever the size of the scatterers, the power re- 
ceived at the radar can be described by a common 
formula. Consider some particular scatterer, say the 


•’Ey H. Goldstein, Radiation Laboratory, MIT. 


196 


ECHOES AND TAUGETS 


yth one. Then the returned signal from this particular 
target is 

„ Pt 

1 rj = (Tj, 

where (xj is the radar cross section of the yth scattercr, 
Pt the power transmitted, G the gain, A the wave- 
length, and Ii the range, o-y differs from the customary 
cross section in that it incorporates the propagation 
factor and hence may depend on the height of target 
and the glancing angle of the incident ray. In consid- 
ering the time average of the total power received by 
the radar we can take the scattering to be incoherent. 
Hence the average radar signal is the sum of Pn over 
all the j scatterers lying within the area illuminated 
by the beam width and pulse length : 


Pr = 


p, G2 X2 


It is assumed that the illuminated area is sufficiently 
large that the sum contains many scatterers and is 
proportional to the size of the area. In that case this 
formula can be written 


Pr = 


PtGn^ , rc 
(4)r)3 ^ 2 


where </> is the azimuthal beam width, r the pulse 
length in seconds, c the speed of light, and a is defined 
as the radar cross section of sea echo per unit area of 
the sea surface and hence is dimensionless. This quan- 
tity o- is a function of many parameters: the state 
of the sea, the glancing angle of the incident beam 
(and therefore the range), the polarization, and the 
wavelength. A comprehensive program is under way 
in the Eadiation Laboratory to check the assumptions 
underlying this formula and to determine the cross 
section o- as a function of these parameters. 

Uhlenbeck has pointed out that the dependence of 
(T on wavelength should be an especially sensitive 
function of the scattering mechanism assumed. For 
drops whose circumference is small compared to the 
wavelength, the scattering should be of the Eayleigh 
type, i.e., varying as 1/A^. If one takes into account 
the lobe pattern of the incident field due to reflection 
on the water surface, the dependence is even faster, 
possibly as 1/A®. On the other hand, if we are dealing 
with reflection or diffraction from large curved sur- 
faces, then a should be substantially independent of 
wavelength or even increase with A. By measuring a 
simultaneously on two or more frequencies, it should 
be possible to decide between these mechanisms. 


Accordingly, such measurements were made in the 
summer of 1944 at Bar Harbor, using the calibrated 
S- and X-band mobile radars belonging to the Wave 
Propagation Group of the Eadiation Laboratory. The 
site elevation was 1,500 ft, and the ranges about 
10,000 yd, so that the incident angles were quite small. 
The constants in the formula for were determined 
as accurately as possible. In addition, the power, pulse 
length, and beam width were made comparable in 
both systems. For relatively stormy sea conditions the 
ratio of o- on the two wavelengths was found to be: 

— = +5 ± 4 db 

0‘S 

for both polarizations. If the Eayleigh 1/A^ law holds, 
the ratio should be -|-18.5 db, which would seem to 
exclude spray drops as the scatterers. 

One of the difficulties of this type of measurement 
is to determine the average level of a signal that 
fluctuates as rapidly as does sea echo. To remove this 
source of trouble, a device has been developed that 
reads the average power directly. It might be de- 
scribed as a gated noise meter. With the aid of this 
instrument we have again begun making measure- 
ments of o- on S and X bands, this time from Deer 
Island in Boston Harbor. The elevation is only 120 
ft, and the ranges are correspondingly small. 

The results obtained so far do not agree in all re- 
spects with the previous data obtained at Bar Harbor. 
When the sea is fairly calm (Beaufort 3 or less), the 
ratio of o-x to is reproducibly given by : 

(7X 

— = +12±2db horizontal 

0‘s 

on horizontal polarization. The scatter is much greater 
on vertical polarization, and the ratio is much smaller : 

0‘x 

— ^ +4 db vertical. 

0‘s 

One set of worth-while measurements has been made 
with a sea that was considerably rougher (Beaufort 
4-5). The ratio was significantly smaller for both 
polarizations : 

o’x 

— = +5 ± 2db horizontal 

0‘s 


— = +2db vertical, 
o-s 

At the time these data were obtained the first 
measurements were made with a calibrated experi- 
mental K-band set recently constructed. Only hori- 


DEPENDENCE OF SIGNAL POWER ON PARAMETERS 


197 


zontal polarization was available. It was found that 

— = 3 to 5 db. 
o’x 

Hence under these sea conditions the increase in a 
on going from S to X is about the same as when going 
from X to Iv. 

An interesting by-product of these measurements 
was the comparison of polarizations, keeping the wave- 
length the same. This ratio was quite variable, rang- 
ing from 

— = — 9db Xband 

(TH 

on X band under stormy conditions, to 

— > -f 25 db S band 

(th 

on S band with a calm sea. In general the ratio de- 
creases as sea becomes rougher and is almost always 
less on X than on S band. 

It is too early in the investigation to attempt a de- 
tailed interpretation of the results. It does seem that 
scattering from small spray drops is not the sole 
mechanism, despite the popular observation that sea 
echo seems to increase rapidly with the appearance 
of whitecaps. Other evidence also seems to confirm 
this. Under favorable conditions sea echo appears as 
discrete signals, moving with the wind, that can be 
tracked for 15 to 20 sec. This seems longer than one 
would expect from a breaking wave. On the other 
hand, reflection from large wave surfaces cannot be 
the whole story either. This is indicated by the fairly 
rapid increase of o- with frequency and by the com- 
plicated changes with polarization. It i^ probable 
that we are dealing with a combination of mech- 
anisms, and it will be a difficult task to unscramble 
the contribution of each to the total signal. 

It should be emphasized that these measurements 
were taken near the coast, though outside the break- 
ers. Conditions on the high seas might conceivably be 
quite different. 

Discussion 

It was stated that individual sea echoes which 
persist for many seconds cannot be caused either by 
specular reflection from an inclined water-air inter- 
face or by random (Rayleigh) scattering from in- 
dividual drops of spray. Instead, an aerated surface 
layer created by a breaking whitecap may persist for 
many seconds and may be responsible for persistent 
echoes. Such a layer constitutes an irregular network 


of air-water interfaces and may give rise to consider- 
able scatter of microwaves. The actual mechanism by 
which such a layer gives rise to a sea echo is likely to 
be different at different sea states. If a large area is 
covered with foam, then ,in the presence of strong 
swell the chief return should be expected from a wave 
crest, and the radar signal would appear to travel 
slowly on the radar screen as the wave crest pro- 
gresses. 

The author stated that so far no consideration had 
been given to such involved mechanisms as the one 
suggested, but added that data already collected might 
well lead to such an investigation. 

It was suggested that several mechanisms, includ- 
ing scattering from droplets, were probably respon- 
sible for sea echo in rough weather. Experiments in 
Britain reported by the British Army Operational 
Research Group showed that echoes from shell splashes 
viewed on an S-band gunnery radar could be resolved 
into two parts. One was from the “^ffioil,^’ a solid wall 
of water with enclosed air bubbles, which could be 
readily distinguished from the superimposed response 
from the larger portion of the splash called the 
‘^‘’plume,’^ which is a region of isolated water drop- 
lets. Echoes from the droplets in the ^^plume’^ region 
were of many seconds duration, and it seemed likely 
that an investigation of the frequency dependence of 
such, scatterers would produce useful results. 

12 3 the dependence of signal 

THRESHOLD POWER ON RECEIVER 
PARAMETERS^ 

This paper deals with the effect on the signal thres- 
hold power of various parameters in the receiving 
systems of radar sets, i.e., with the minimum signal 
power necessary for visibility. Although this is a diffi- 
cult problem and all the important factors entering it 
are not known, it is felt that at least qualitatively, 
and sometimes quantitatively, a fairly good answer 
can be given at present. First of all it is necessary to 
define some of the parameters involved in ordinary 
radar reception. When a signal is reflected from a 
target the power entering the receiving system may 
be written in the following form: 

{4.TrYR^ 

where 0 , X, and o- are the antenna gain, radar wave- 

®By J. L. Lawson, Radiation Laboratory, MIT. 


198 


ECHOES AND TARGETS 


length, and target echoing area or cross section, re- 
spectively. Pt is tlie transmitted power and P the 
target range. This is, of course, the free space formula. 
The propagation conditions can be conveniently lump- 
ed into a multiplicative factor, which in the follow- 
ing arguments is of little concern. To determine the 
maximum range capability of the radar set, it is nec- 
essary to determine how large Pr must be in order to 
be detectable. It is then possible to calculate the maxi- 
mum range capability of the radar set from the above 
formula, on writing it : 

It has been common practice to assume that Pr min, 
or the signal threshold power, is of the order of magni- 
tude of the noise power in the radar receiver. This is 
certainly true ; it is of the order of magnitude of that 
noise power but is not generally equal to it. This 
paper deals with the various factors in the receiving 
system and display system which affect Pr min- 

A few of the things that affect Pr min are 

1. The capabilities of the human observer. 

2. The properties of the display system on which 
the signal is presented to the observer. 

3. The type of interference which prevents the de- 
tection of an extremely small signal. 

This interference is not always receiver noise. There 
are storm cloud echoes and similar interferences, but 
this discussion will deal only with the case in which 
receiver noise is the limiting factor. 

It is useful to define the signal threshold power. 
A good deal of work has been done on this question, 
both theoretical and experimental, and in the course 
of events a satisfactory criterion has been developed. 
There is not a defined minimum threshold power 
above which the signal is always seen and below which 
it is never seen. One finds experimentally that if the 
signal power S is plotted against the percentage of 
cases in which the signal is correctly identified, a 
‘^‘betting curve’’ is obtained. It takes several times as 
much signal power to obtain a correlation of 90 per 
cent as it does to obtain a correlation of 10 per cent. 
In this paper the signal power which permits a cor- 
relation of 90 per cent will be considered the thresh- 
hold signal. 

Two main types of displays are used in radar 
sets, the A-scope display and the jjlan position 
indicator [PPI] or intensity-modulated display. 
In the A-scope display there is presented a trace 


in which the apparent range of the target appears 
as abscissa and the amplitude of the received echo 
as ordinate. Along the trace the ever present 
receiver noise appears ; where the target is there 
will be a larger average deflection. In experiments 
on the A scope an artificial echo of controlled am- 
plitude and range was introduced into the receiving 
system. This artificial echo was so introduced 
that it could fall into any one of several fixed 
range positions. Usually six fixed range positions were 
used. The observer then attempted to call the position 
occupied by the signal. ^‘Betting” curves were then 
drawn and Sqq (90 per cent signal threshold power) 
determined. This is the signal power, usually meas- 
ured in terms of noise power in the receiver. Between 
zero correlation and 90 per cent correlation a change 
in signal power of perhaps 5 db is usually required. 
This is quite a large spread, and it is very difficult 
to determine accurately because of the statistical 
fluctuations. Ordinarily in running such a curve a 
single threshold power measurement requires 50 to 
100 observations. This laborious and lengthy process 
of obtaining signal threshold is necessary to remove 
the subjective element. The results obtained in this 
way are remarkably constant and consistent among 
different observers. They do depend on other factors, 
however. They depend both experimentally and theo- 
retically on the number of range positions, and it 
becomes necessary to indicate the type of variations 
which obtain. A ^^6 position, 90 per cent point” has 
already been defined for this experiment. This is taken 
as the standard of reference denoted by 0 db. 
for a position” experiment is +0.8 db experi- 

mentally and +1.5 db theoretically. Sqq for an '‘N 
position” experiment is +1.0 db both experimentally 
and theoretically. for the ^^2 position” experiment 
is — 2 db experimentally and — 1/2 db theoretically. 
In this last case the experimental improvement is due 
in part to the statistical difference and in part to 
the greater ease with which the observer can con- 
centrate on the range positions. 

In spite of these variations it is felt that any one 
of these definitions is representatively good. For con- 
venience the Sqq for the position” experiment has 
been chosen, since it gives a sufficient number of posi- 
tions so that statistical determination of Sqq can be 
obtained with reasonable ease. It is possible to make 
the same correlation trials for the intensity-modulated 
PPI as for the A scope. The signal is put at any of 
a number of range positions which are fixed in azi- 


DEPENDENCE OF SIGNAL POWER ON PARAMETERS 


199 


muth. Scanning conditions may be included if de- 
sired. Some factors which affect the signal threshold 
power will now be enumerated, and the magnitude of 
their effects described. 

The first such factor is the noise figure of the re- 
ceiver. In brief, this is simply a multiplicative factor 
which would go with any of the other determinations 
made. The noise figure of the receiver specifically 
measures the amount by which that receiver is noisier 
than the best theoretical receiver. Ordinarily this noise 
figure runs to the order of 10 db, which means that 
the receiver is something like 10 times as noisy as 
the theoretically perfect receiver. As we are dealing 
with signal threshold power in terms of the receiver 
noise power (the latter being a universal parameter) 
it is only necessary to determine the noise figure of a 
given receiver in the field to determine what sort of 
input signal power is necessary. 

The second factor affecting the signal threshold is 
the intermediate frequency or the radio frequency 
bandwidth B of the receiving system. B represents 
specifically the narrower of the two. This bandwidth 
will affect the signal visibility in a way which will be 
discussed presently. The third quantity is the video 
bandwidth & of the receiver. At one time it was thought 
that the video bandwidth and the i-f bandwidth were 
equivalent, but this is not at all true. Between the 
i-f and the video systems there is a second detector 
which is a nonlinear element, which causes frequency 
conversion to take place. This causes the video band- 
width to have an entirely different action from that of 
the i-f bandwidth. A third factor is the sweep speed 
of the scope, denoted by small s. The sweep speed has 
an important effect which is nearly equivalent to that 
of video bandwidth. Another parameter is the time 
interval during which the signal is actually presented 
to the observer. This quantity will be represented by 
the letter T and called the signal presentation time. 
In addition to these there are several other factors 
connected with contrast effects in the presentation 
and the scanning variables. 

The first four variables mentioned apply to the 
geometry of the system, and geometrical scaling argu- 
ments can be applied to these quantities. One of these 
variables can thus be eliminated at the start by using 
not the pulse length r, but the product 5 X t as a 
variable. Similarly, the other variables are B X t, 
h X T, and N X t. These quantities have a definite 
physical significance. The sweep speed multiplied by 
the pulse length is simply the length of the signal on 


the scope and can be expressed in millimeters if de- 
sired. B X T is the i-f bandwidth times the pulse 
length and turns out to be a simple number. This is 
a number which will affect the signal visibility curves. 
Similarly the video band\yidth 6 X r is another num- 
ber. The signal power multiplied by the pulse length 
is simply the energy of the signal per pulse, and so 
on. These variables are essentially geometrical para- 
meters. The pulse repetition frequency and the signal 
presentation time are statistical parameters and must 
be treated in a statistical way as will be shown. 

The first geometrical factor to be considered is the 
i-f bandwidth. The interesting factor is the behavior 
of signal and noise. Independently, these are known 
quite well. With respect to noise the power response 
is proportional to the bandwidth. However, the re- 
sponse to a signal of a particular length, once there 
has been obtained a bandwidth which is adequate for 
the transmission of the pulse, will be essentially in- 
dependent of the bandwidth. When the bandwidth is 
very narrow the voltage of the output pulse is propor- 
tional to the bandwidth of the receiver. A curve can 
be drawn which is essentially the signal-to-noise power 
response curve, which for wide bandwidth will be 
proportional to the signal threshold power, while for 
narrow bandwidth it will be inversely proportional to 
the bandwidth. This is exactly the form of curve ob- 
tained experimentally. The optimum bandwidth is 
found to be approximately 1.2 times the reciprocal of 
the pulse length. The noise power in the receiver is a 
very poor single criterion as to how small a signal can 
be seen. For example, with a bandwidth of 1 me for 
l-jutsec pulse a signal about 2 db below the noise 
can be seen. But if the i-f bandwidth is 10 me for a 
l-fisec pulse, a signal is visible 7 db below noise. If 
the i-f bandwidth is too small, even a signal equal to 
noise power is invisible. In general, therefore, signal 
threshold power is rated in decibels above the receiver 
noise power for a particular value of B (usually B 
= 1/r), since this provides a universal scale. 

For the video bandwidth the situation is more com- 
plicated. A good deal of theoretical work can be done 
on this problem, but the experimental data do not 
confirm the theory. The reason is that the video band- 
width is already effectively narrowed by the effect of 
sweep speed. Video bandwidth effects can be observed 
when the sweep speed is very fast, where s X t (the 
pulse length on the scope) is of the order of a milli- 
meter or so. Under these conditions video bandwidth 
narrowing always reduces the signal visibility and in- 


200 


ECHOES AND TARGETS 


creases the signal threshold power. There is a real 
difference between the video bandwidth and the i-f 
bandwidth in the following respect. Decreasing or 
increasing the i-f bandwidth causes the components of 
low-frequency noise in the video to change proportion- 
ally. Video narrowing, however, does not change the 
low-frequency video noise components. Therefore, the 
reduction in signal visibility with video narrowing is 
less pronounced than with i-f narrowing. 

The human eye cannot distinguish between two ob- 
jects which are closer together than about 1 minute of 
arc. If the light intensity contrast is limited, two ob- 
jects cannot be resolved even at a much greater angular 
separation. When the separation approaches approxi- 
mately ^ of a degree, the best visibility will be ob- 
tained for the smallest contrast. Thus, the action of 
the human eye can be regarded as that of a filter which 
preferentially selects those frequencies having a period 
of the order of of a degree on the scope. At normal 
viewing distances this value of angular separation is 
of the order of 1 mm linear separation. Since the 
screen behaves like a linear transformation between 
the video signal and the light transmitted to the eye, 
this filter action of the eye is exactly equivalent to a 
video filter whose maximum pass frequency corre- 
sponds to 1 mm divided by the sweep speed s. For most 
presentations, where the pulse length is considerably 
shorter than 1 mm on the scope, this effective video 
narrowing action of the eye is usually much more im- 
portant than the effect of video bandwidth in the re- 
ceiver. It is to be noted, however, that video bandwidth 
effects in the receiver can be observed when the sweep 
speed is sufficiently fast for proper delineation of the 
pulse. There is now a considerable amount of experi- 
mental evidence to support this rather simple picture 
of the combined effect of video bandwidth and the 
resolution properties of the eye. 

Because of this property of the eye, if the viewing 
distance is maintained constant, a large diameter PPI 
will be more sensitive in the detection of signals than 
a small one. A magnifying glass will produce an effec- 
tive increase in sensitivity on the small scope at the 
expense, however, of a restricted searching area. 

The focus on the PPI or A scope also acts like a 
video narrowing device. If the tube is defocused along 
the range scale, equivalent video narrowing will take 
place by an amount which is dependent upon the spot 
size. However, because of the effect on the human eye 
a loss in signal visibility will not occur until the de- 
focused spot is larger than approximately 1 mm. 


Dcfocusing to this extent is certainly disadvantageous 
in the ultimate discrimination of two close radar tar- 
gets, and for this reason good spot focus must be 
maintained. 

In signal detection it is clearly necessary that the 
average signal deflection voltage be as large as the 
average noise fluctuation in the absence of signal. This 
is a purely statistical problem susceptible to theoretical 
analysis. Calculations show that the quantities which 
determine signal visibility, apart from the geometrical 
factors just described, are the total number of sweeps 
on which the signal is visible and the total number of 
sweeps on which only noise is visible. It is assumed 
that for these sweeps integration or averaging takes 
place. This result is confirmed experimentally with 
two restrictions. The total number of signal pulses is 
given by T X PRF (pulse repetition frequency), and 
the signal threshold power is found to vary inversely 
with both PRF and T. While this holds for all values 
of PRF under investigation (12.5 to 3,200 c) it holds 
only for a limited region in T (approximately 0.05 to 
3 sec). The reason why the integration is not satis- 
factory outside these limits of T are related to the 
maximum dicker frequency detectable by the eye. For 
times shorter than perhaps 0.05 sec additional sweeps 
containing only noise will be integrated. Likewise, for 
T greater than 3 sec the eye and brain do not appear 
to integrate properly all the individual voltages. In 
other words, the system has incomplete memory. It 
has been found that the maximum system integration 
time (usually of the order of 6 sec) can be increased 
appreciably by operator practice. With a considerable 
amount of experience a good radar operator can effec- 
tively integrate for times as long as V 2 min. It is to 
be noticed that because of this integration in the eye 
and brain of a radar operator other methods for pro- 
viding integration, such as P-7 screens or photographic 
integration, will fail to provide substantial benefit 
unless their effective integration time exceeds several 
seconds. This conclusion is borne out experimentally. 

In the radar scanning problem the same factors 
must be considered as have already been discussed, 
but, in addition, one must investigate factors peculiar 
to scanning. Among these are the rotation speed of the 
antenna, the beam width of the set, etc. It has been 
found, however, that the statisical problem met with 
in scanning is quite similar to that encountered in the 
absence of scanning. The complete system integration 
depends on two factors: the number of pulses inter- 
cepted by the radar beam during one traversal of the 


DEPENDENCE OF SIGNAL POWER ON PARAMETERS 


201 


target, and scan-to-scan integration. If the scanning 
rate is sufficiently rapid (faster than 10 rpm) the 
signal visibility will be independent of the antenna 
rotation rate. Faster rotation rates intercept a smaller 
number of pulses for each revolution, but there are a 
greater number of scan-to-scan integrations which just 
make up for the deficit. However, below the critical 
speed of about 10 rpm, scan-to-scan integration will 
not take place, and the signal threshold power will be 
proportional to the square root of the antenna rotation 
rate. This improvement in signal visibility at slower 
scan rates will continue until the antenna is on the 
target, during each revolution for approximately 6 
sec, whereupon the visibility is essentially that of a 
‘^searchlighting’^ set. Thus the total scanning loss is 
given by the rather simple formula 

Loss = 1 , 

where Ft is the fraction of time that the system is on 
target during the scanning procedure. Ordinarily this 
scanning loss amounts to approximately 10 db in an 
average radar system, requiring a signal perhaps 10 
times as large as the necessary amount for detection 
while searchlighting. It is important that this formula 
be used only where scan-to-scan integration takes 
place. 

Discussion 

While this paper has specifically been limited to 
noise considerations, it seemed reasonable to hope that 
the same general considerations could be applied in 
determining the visibility of signals in various types 
of clutter, in particular the simpler types which are 
echoes from rain and snow. If the mechanisms involved 
were more thoroughly understood, the fundamentals 
of the problem would be understood too and could be 
put together in a coherent form. 

The shape of the response curve has been considered 
by the author and is known to have some effect, but 
the experimental approach to various shape factors 
has been rather limited. In the work presented here 
the response curve of the receivers involved has been 
that of a so-called double-tuned circuit, whose ampli- 
tude response is proportional to 

[-©■]“. 

where <o is the frequency difference between the fre- 
quency under measurement and the center of the band. 


ft)o is the V 2 bandwidth. The difference between this 
response curve’s performance and that of a multiply 
narrowed, synchronously tuned, intermediate ampli- 
fier, which has Gaussian response, was not observable 
experimentally. Theoretically also, there is little dif- 
ference. It is felt that the 'considerations may not apply 
in extreme cases of sharp-edged amplifiers or in single 
single-tuned circuits but that in other cases the same 
answers do apply. 

The question was raised as to the dependence of 
signal threshold on pulse recurrence rate. In all the 
other parameters the visibility of the signal is pro- 
portional to the signal energy. The author found that 
for a given average power the visibility is distinctly 
better if you concentrate more energy into, each pulse 
and separate the pulses by longer intervals. In other 
words, the threshold is proportional to the energy per 
pulse but inversely proportional to the square root 
of the repetition frequency. This settles a disagree- 
ment between two groups, one of which believes visi- 
bility would be found independent of pulse repetition 
rate and the other that it depends on average energy. 
The answer lies between the two views. In this matter 
of visibility it is interesting to recall that the first suc- 
cessful radar, which was giving ranges up to 25 miles 
in 1936, had a receiver bandwidth of about 200 kc and 
a pulse length of 5 jusec, a combination which lies on 
the peak of the maximum visibility curve. The pulse 
length on the radar screen was about 3 mm. The curve 
for optimum visibility peaks at 1 mm and does not 
decline very rapidly for longer pulses, so that, too, was 
near the optimum value. The first production radar for 
use in the fleet had a pulse length of about 3 /xsec and 
a bandwidth of about 300 kc, which is again on the 
peak of the visibility curve, and its visible pulse was 
about 2 mm long on the screen. This was of course not 
entirely accidental but was fortunate, nevertheless. 
The preproduction model of this radar was built in 
1938. 

The author discussed the effect of fluctuating sig- 
nals in scanning as distinct from the steady signals 
which had been employed in the experiments described. 
In the case of signal fluctuation, it is necessary first to 
define the signal amplitude in such a way that analy- 
sis is applicable. Employing the average value as a 
criterion, the visibility of fluctuating signals may ac- 
tually prove greater than for steady signals. If the 
peak value of a fluctuating signal is taken as the signal 
threshold power, the visibility is probably poorer than 
for a steady echo, but it is felt that the result would 


202 


ECHOES AND TARGETS 


be again essentially independent of the scanning speed, 
as long as it is high enough to cause pulse-to-pulse and 
scan-to-scan integration. The limit, however, may 
occur at 20 rpni instead of 10 rpm. 

One variable has been omitted which has proven 
puzzling. This is the target speed. What really con- 
stitutes a scan-to-scan integration ? If the target moves 
the distance of one spot diameter in a scanning period, 
is it still integrated ? It would seem to be so integrated 
provided the observer is able to perform as an aided 
tracker, i.e., can appreciate a change in linear motion. 
If it is not integrated, one would expect to find a 
difference in signal threshold depending on the target 
speed, probably in direct proportion to the square root 
of target speed. Some experiments have been made on 
simulated echoes of this variety, and there was some 
indication that targets of higher velocity are definitely 
harder to see, but this cannot be considered quantita- 
tively established. Signal fluctuation, however, is im- 
portant, and it is felt that, in general fluctuating tar- 
gets with cross sections defined on the basis given in 
the following paper are harder to see by perhaps 2 db 
but that this estimate is not affected by any arguments 
about scanning. 

There was another inquiry concerning the explana- 
tion of the Watson effect observed occasionally at very 
close ranges when the background noise was so large 
the normal signal could not be detected. This con- 
sisted of an inverted signal smaller in amplitude than 
the background noise which could be observed to a 
range of almost 100 yd in sets which had a direct wave 
extending to 3,000 to 4,000 yd. In these cases the signal, 
instead of appearing as a small inverted V, showed up 
as a small upright V, approximately Vs the amplitude 
of the initial noise. This effect had been often reported 
on short-range targets. The author considered this to 
be a form of receiver saturation. Another group had 
been troubled by the same phenomenon and had at- 
tributed it to receiver saturation in which there was 
blocking of the i-f amplifier during a portion of the 
time. 

12 4 RADAR SCATTERING OVER 
CROSS-SECTION AREA^* 

It is of great interest to determine the cross-section 
values of aircraft, not only in order to attempt predic- 
tion of ranges on these aircraft, but also to make pos- 
sible the design of radar equipment which will utilize 
these factors a little better. The instantaneous pattern 

‘*By J. L. Lawson, Radiation Laboratory, MIT 


of reflection properties of an airplane is very complex. 
It depends upon the frequency, type of aircraft, and 
certain other factors, such as propeller rotation. The 
pattern has an extremely complex lobe structure which 
depends essentially upon the lengths of the plane’s 
structure in terms of wavelength and upon the areas 
of specular reflection, that is, reflection from fairly 
large, flat, mirror-like surfaces found in most aircraft, 
such as the sides, bottoms, or wing surfaces. 

It would be possible to define the instantaneous 
cross-section area as a function of the angle from the 
airplane, but this kind of thing would be purely aca- 
demic, since actually the airplane is moving. In the 
early part of this work an attempt was made to derive 
a cross-section number which would apply to the actual 
radar performance on an airplane in flight. The scat- 
tering cross section may be calculated from the re- 
lation 

" ~ PtGV ’ 

where the quantities are measured in free space. The 
symbols are defined in Section 12.3. They are all easily 
measurable except Pr, the received power. This was 
measured by injecting into the system, with a signal 
generator, an artificial echo which was matched to the 
size of the airplane echo. 

In pratice, o- is necessarily a function of time, and 
for lack of a better criterion the following procedure 
was adopted. The signal generator reading was con- 
tinuously matched to the size of the aircraft echo and 
recorded for successive 3-sec intervals. The signal 
measured in decibels above receiver noise power was 
plotted against range. On a logarithmic scale such a 
plot should be a straight line whose variation is 40 db 
for a factor 10 in range. This is actually found, pro- 
vided one draws a line through the average of the 3-sec 
interval points. From moment to moment the fluctua- 
tion is rather high, but nevertheless a good average 
line can be drawn. 

It is now possible to define a cross section by the 
condition that its value is exceeded in one-half of 
these 3-sec intervals, and this appears to be an easy 
operational way of obtaining cross sections. However, 
this still does not represent what could be called the 
average value for each 3-sec interval. It was found very 
early that it was very difficult to adjust a signal gen- 
erator to the average value of the signal. It is much 
easier to adjust to the top value that has occurred dur- 
ing an interval. The reason for this is that the signal 
is quite often fuzzy and filled in by propeller modula- 


RADAR SCATTERING OVER CROSS-SECTION AREA 


203 


tion. Therefore, the figures represented here are in 
general the highest values that occur during the 3-sec 
interval. For this reason we have attempted to see how 
the value of o- depends upon the interval timing and 
whether or not it is permissible to put this value into 
range formulas in the usual way. A rough working 
model is the following: If these cross-section values 
are reduced to 60 per cent, they may be used in the 
range formula presented in the previous paper to ob- 
tain the correct operational radar range. The cross 
section averaged over the lobe structure in the front 
aspect or tail aspect of a plane would be lower than 
these values by probably 50 per cent. 

Some representative figures are as follows : Fighter 
aircraft usually vary from 1 to 200 sq ft; medium 
bombers, B-18, Beaufighter and similar aircraft range 
from 4 to 600 sq ft; and heavy bombers, B-17, 800 
sq ft. The larger bombers such as the B-29 have not 
been measured but are estimated to be of the order 
of 1,200 sq ft. 

Discussion 

To a question regarding the wavelength dependence 
of aircraft cross sections, the reply was that such a 
dependence was a function of the structure of the air- 
craft. Outside surfaces having rounded structures such 
as wings, wires, and similar members have a cross 
section which is essentially independent of wavelength 
and produce random scattering, provided the frequen- 
cy is high enough. As the frequency is lowered, reso- 
nances in the structure of the airplane and differences 
in the wings may appear. This might possibly cause 
differences with regard to polarization. At S-band and 
higher frequencies there seems to be little dependence 
upon frequency. These figures have been checked at 
S and X bands with essentially the same results. No 
sensible dependence on polarization was observed, in- 
dicating that at S-band or higher frequencies, this sort 
of cross-section value will apply. 

Ohio State University is conducting an extensive 
program of cross-section measurements on various 
types of aircraft for a variety of frequencies up to 500 
me. Measurements are made for all aspects of the air- 
craft and for both vertical and horizontal polarization. 
The procedure used is to scale the aircraft down to a 
convenient model size and to use a correspondingly 
higher frequency. 

The results of these measurements exhibit a confus- 
ing lobe structure. In order to give an overall descrip- 
tion of the behavior of the cross section, a reasonable 
procedure must be found for averaging the data. This 


has been attempted. At 100 me, the specular reflections 
are not particularly marked, though the cross section 
does increase in directions perpendicular to the axis 
of the aircraft. There is still fairly strong scattering 
in all directions. At 500 ipe the echoes are almost en- 
tirely due to specular reflection. The dependence on 
polarization is stronger at the lower frequencies. 

The author commented that simultaneous measure- 
ments of average values for different polarizations 
showed them to be about the same but that instan- 
taneous pulse-to-pulse photographs of a single target 
with two different polarizations showed them to be 
quite different at a given instant. 

An inquiry was made as to whether any correlation 
had been made between radar cross section and type 
and dimensions of aircraft. A report was mentioned 
which attempted to show that scattering cross section 
was proportional to wingspread. The results of the 
author’s group did not appear to correlate with wing- 
spread, but the fuselage is important, and both factors 
must be significant. Experiments had been made with 
controlled flights in which the aircraft was flown 
straight toward or away from the radar site. It was 
believed that, because of normal wind conditions and 
such factors as yawing in flight, the results obtained 
represented an average over an angle of about 10° for 
both front and rear aspects. Some measurements at 
45° aspects were made which showed a drop of about 
1 or 2 db for most aircraft. Some aircraft showed a dif- 
ference between average head and average tail aspect 
of about 1.5 to 1, and the figures previously quoted 
represented an average between the two aspects. When 
the aircraft in turning presents a broadside, specular 
reflection occurs, and this side flash often exceeds the 
ordinary signal by 100 times or more. 

The comment was made that the measurements de- 
scribed seemed to have been made entirely with track- 
ing radars using A-scope presentation. What would be 
the probable effects of such fluctuations on radars with 
search type presentation? The author believed that 
such fluctuations would affect search-type radars 
when scanning slowly but that no serious effect had 
been observed at scanning speeds as low as 2 rpm. 
When the cross-section figures given were used with 
a 2-db reduction for average values, the predicted 
ranges were in agreement with the observed ranges 
even on scanning or search type radars. This is prob- 
ably not true at certain longer wavelengths for which 
the lobe structure is such that an aircraft can ^Tide” 
a null for an appreciable time interval. At micro wave- 


204 


ECHOES AND TARGETS 


lengths, the lohes are so close together that it becomes 
practically impossible for an aircraft to remain in a 
null for an appreciable time. 

It was inquired whether drops of more than 2 db 
were to be expected for other aspects, such as 45 
degrees. While a complete series of measurements had 
not yet been made by the author’s group, measure- 


ments on three or four aircraft in various aspects had 
revealed no drops below 2 db. Although the calibration 
had been carried out entirely with signal generators, 
standard targets consisting of corner reflectors and 
spheres had been set up later and produced results in 
substantial agreement with the theoretically predicted 
values. 


Chapter 13 

ANGLE-OF-ARRIVAL EXPERIMENTS 


13 1 ANGLE-OF-ARRIVAL MEASUREMENTS 
IN THE X BAND^ 

T he puiirosE of this work was to observe the varia- 
tion in angle of arrival of waves in the X band. No 
simultaneous air sounding data were taken although 
general weather observations were made. 

The method of measuring the angle of arrival makes 
use of a very sharp-beamed antenna (Figure 1) 
mounted so that it may be mechanically tilted back 



Figure 1. Sharp-beamed antenna used for measuring 
the angle of arrival. 

and forth about its center thus sweeping the beam of 
the antenna through an arc which may be set to include 
the expected angle of arrival of the incoming signal. 

The sharp-beamed antenna has been used to measure 
the angle of arrival of waves from a distant trans- 
mitter over an optical path where both a direct wave 
and a water-reflected wave are present. If the output 



kio SEC-^ TIME A-t>B (RECORD 2) 

Figure 2. Variation in signal intensity during scan. 

A, direct ray only. B, direct and reflected rays super- 
posed. 

of the receiving antenna is fed to a receiver and this 
receiver is fitted with a recording type output meter, 
records of the type shown in Figure 2 will be obtained 
as the antenna scans. Record 1 will be obtained if only 
a single, direct wave is arriving at an angle correspond- 

*By W. M. Sharpless, Bell Telephone Laboratories. 


I 

ing to the mid-point of the antenna swing. The dis- 
tances between peaks of maximum amplitude along 
the record will then be equal. A shift in the angle of 
arrival of the wave would appear on the record as a 
change in the spacing between the peaks. If two 
separate waves, direct and reflected, are arriving 
simultaneously, the record will appear something 
like record 2. 

The actual antenna used for the measurement is a 
section of a parabolic cylinder arranged so that its 
beam at the center of swing is pointed directly at the 
transmitter. This is also the angle at which waves 
arrive on a normal day. A normal day has been taken 
as one when the angle of arrival is the same (within 
the accuracy of the measurements) as that calculated 
from actual earth geometry and when free space field 
is received from the direct wave. 

The physical position of the antenna may be held to 
approximately 1/100 degree by the use of a plum-bob 
line dropped from the top of the 20-ft antenna to the 
base. Possible errors in reading the records, however, 
limit the expected relative accuracy to about 1/60 
degree. Slight errors in the actual building of the 
antennas and in the locating of the feed limit the 
final accuracy to what is believed to be 1/25 degree. 

The horizontal angle of arrival is measured with a 
duplicate antenna turned 90 degrees from the vertical 
with its flat side toward the ground. The accuracy of 
measurement is the same as in the vertical plane case. 

The entire equipment, including the two scanning 
antennas, other reference antennas, the receiving 
equipment, and the receiver building are located on 
a rotatable platform which is 25 ft in diameter. This 
equipment, located on top of Beer’s Hill, New Jersey, 
may thus be pointed toward any of several transmitters 
and comparisons made of the angle of arrival from 
each transmitter. 

Observations during the summer of 1944 have been 
made on two optical paths shown in Figure 3: (a) A 
24.1-mile path partly over land and partly over water 
between New York City and Beer’s Hill, New Jersey. 
The normal reflecting point for the reflected ray on 
this path is in the salt water of Raritan Bay; (b) a 
12.6-mile path between Beer’s Hill and Deal, New 
Jersey. This path ijs all over gently rolling land. The 


205 


206 


ANGLE-OF-ARRIVAL EXPERIMENTS 



MILCS 


BCCR*S HILL 



MILCS 


Figuee 3. Propagation paths, (top) Beer’s Hill to New York and (bottom) Beer’s Hill to Deal. 


transmitters at both Deal and New York radiate waves 
polarized at 45 degrees so that either vertical or hori- 
zontal polarization may be used at the receivers. 

Results of angle-of-arrival measurements made dur- 
ing the summer of 1944 indicate that on both the Deal 
and New York circuits the greatest variation of angle 
of arrival in the horizontal plane was ±1/10 degree. 
Times were found when the angle of arrival remained 
as much as 1/10 degree east for short periods on the 
New York circuit, but for the most part the horizontal 
angle of arrival normally fluctuated ±1/10 degree 
from the normal day direction on both the Deal and 
New York circuits. The maximum variation in the 
vertical angle of arrival on the direct wave on the 
New York path has been 0.46 degree above that ob- 
served on a normal day, while the reflected wave has 
come in as low as 0.17 degree below the normal re- 
flected wave. (On a normal day the reflected wave on 
the New Y^ork path should be, by calculations, 0.33 
degree lower than the direct wave.) 

There does not seem to be any correlation between 
the variation in angle of arrival on the direct wave 
and the reflected wave. These variations do not as a 
rule occur together. At the time when the greatest 
deviation in the reflected wave was present the direct 
wave was coming in normally. Also, when the direct 
wave was up 0.46 degree, it was apparently being 
trapped, and at that time no reflected wave was re- 
ceived. The greatest spread observed between the 
direct and reflected wave was 0.75 degree (normal 
0.33 degree). At this time the direct wave was 0.35 
degree above normal while the reflected wave was 0.07 
degree below normal. The near proximity of Staten 
Island to the path normally taken by the reflected 
wave on the New York path has probably contributed 
to complexities of the results obtained on this circuit. 

The vertical angle of arrival on the Deal circuit has 
not varied as greatly as on the New York circuit. The 


greatest change in angle has been an increase of 0.28 
degree in the direct wave angle of arrival. The reflected 
wave is not of sufficient magnitude to be observed on 
the Deal circuit. 

Height run experiments were conducted to obtain a 
value for the effective coefficient of reflection for the 
Deal path. An oscillator was hoisted up and down the 
175-ft tower at Deal and the resulting received field 
recorded at Beer^s Hill. The field was found to vary 
3.6 db from maximum to minimum (3 maximum val- 
ues and 2 minimum values) as the oscillator changed 
height, which indicates an effective coefficient of reflec- 
tion of 0.2. This means that the received reflected wave 
is 5 times weaker than the direct or 14 db down. The 
distance above ground at which the maximum and 
minimum were obtained were noted on the receiver 
record, and from these the height of the effective reflec- 
tion layer was obtained. This height was found to be 
approximately 100 ft above average ground level. 

This experiment is to be repeated when leaves have 
fallen from the trees to determine if the effective re- 
flection coefficient or the height of the reflecting layer 
has changed. 

Rain has been found to influence the X-band cir- 
cuits in a manner such as to cause a lowering of the 
received fields. During very heavy downpours, we have 
experienced as much as 0.8-db attenuation per mile 
of path length on both the paths. We have no way of 
knowing how much rain was falling over an entire 
path, but the figure of 0.8 db per mile represents the 
maximum value of lain attenuation so far recorded on 
our circuits. 

Only part-time observations have been made on this 
project, and the results reported are based on such 
observations. It is not known, therefore, if more ex- 
treme conditions than those reported have existed at 
times when no observations were being made. 

We expect to continue work on propagation and 


ANALYSIS OF ANGLE-OF-ARRIVAL MEASUREMENTS 


207 


angle-of-arrival studies through next year. Records 
made to date are now being studied in detail, and a 
report will probably be written covering this work. 

13 2 meteorological analysis of 

ANGLE-OF-ARRIVAL MEASUREMENTS" 
Purpose 

Recent experiments on propagation in the X band 
conducted by Bell Telephone Laboratories [BTL] 
have indicated that the angle of arrival of microwaves 
may be considerably at variance with that computed 
on the basis of rectilinear propagation. Deviations as 
large as 0.46 degree from true bearing^ were measured 
during the summer season over a 24-mile path, partly 
over land and partly over water. The deviations found 
experimentally exceed considerably the tolerances spec- 
ified on angle of elevation, azimuth, and height deter- 
mination in present military characteristics on fire- 
control radar equipment. 

An analysis of propagation from the meteorological 
point of view has been undertaken to determine 
whether deviations from rectilinear propagation can 
be explained by, and predicted from, meteorological 
data and whether observed extreme deviations can be 
realized from plausible meteorological stratification. 
The Bell Laboratories^ experimental angle-of-arrival 
measurements made during the summer of 1944 have 
been compared with deviations evaluated from mete- 
orological data obtained concurrently by the Signal 
Corps though not coordinated at the time with these 
experiments. The current paper is intended to report 
the results of this study and the procedure utilized in 
the analysis and, in turn, to establish a framework 
for interpreting further propagation experiments of 
this type. 

13.2.2 Theory 

The equations of propagation can be written in a 
form such that the angle of departure of the radiation 
at the transmitter (the direction of the normal to the 
wave front) and the angle of arrival at the receiver 
can be written as functions of the meteorological 
stratification and the constants of the installation (dis- 
tance between and heights of transmitter and re- 
ceiver). The solution of the equations of motion is 

"By George D. Lukes, Signal Corps Ground Signal Agency. 

®The term “true bearing” as used in this paper refers to the 
vertical angle between the horizontal and a line perpendicular 
to the wave front at the receiving point. 


given below by the use of an electromagnetic wave 
velocity profile obeying a radial power law. The re- 
lation of the exponent m in this power law to the 
excess modified refractive index M is then deduced. 
The power m in the velocity profile equation is as- 
signed the definition of ^‘'meteorological stratification 
parameteiV^ since it determines the change of modi- 
fied index of refraction with height. 



Figure 4. Geometry of a ray in the atmosphere. 


From Figure 4, 


de 


dr 


r tanjd 


ds 

~b 


( 1 ) 


Introduce the electromagnetic wave velocity profile 

( 2 ) 


r\m 

b. 


Hence, 



where 

6(/5 — a) 

s = 

1 — m 

(3) 


COS ^ = l-j cos a. 

(4) 

SnelFs 

law states that 


Then, 

Vo V 

b cos a r cos 13 

(5) 

and 

(1 — m)dr = r tan (3dl3 

(6) 


ds d^ 

b 1 — m 

(7) 

Now 

where 

r = b + h, 

h^b. 

(8) 


208 


ANGLE-OF-ARRIVAL EXPERIMENTS 


The excess modified refractive index 71/ is given by 
nr 

10-6 = — -I 

= + (9) 

If now the relation for the distance s is solved simul- 
taneously with the equation stating SnelFs law of 
refraction, we have the angle of arrival a as a function 
of the excess modified refractive index il/, uniquely 
relating the angular deviation from true bearing to 
the distribution of modified refractive index required 
to produce that deviation. 

13.2.3 Analysis of the BTL New York- 
to-Beer’s Hill Circuit 

The results obtained by Bell Telephone Laboratories, 
Inc., on measurements of the angle of arrival of micro- 
waves in the X band are contained in two BTL re- 
ports.^’2 The New York-to-Beer’s Hill propagation 
circuit proved to be the more suitable for the meteor- 

NEW YORK CITY 

140 WEST ST 



ological analysis of angle of arrival. On this path the 
transmitter was located on the New York Telephone 
building at an elevation of 492 ft above mean sea level ; 
the receiver was erected on top of Beer’s Hill at an 
elevation of 353 ft. The propagation path had a length 
of 24.08 miles and ran several degrees east of north 
from Beer’s Hill to New York. The bearing from re- 
ceiver to transmitter on this circuit on the basis of 
true earth geometry is 0.11 degree below zero eleva- 
tion angle of Beer’s Hill. 

During the summer of 1944 a limited number of 
vertical temperature and humidity soundings were 
secured by personnel of Wave Propagation Studies, 
Evans Signal Laboratory, at a 400-ft radar tower in 
Oakhurst, New Jersey. The location of the tower is 
shown on the map in Figure 5. The tower stands on a 
hill 128 ft above mean sea level. The limit of observa- 
tion is 375 ft above the base of the tower; hence the 
absolute elevation was 503 ft. It follows that soundings 
over the height of the tower sample the atmosphere 
between approximately 11 ft above the transmitter and 
225 ft below the receiver. 

13.2.4 Angle of Arrival Deduced from 
Type Cases of Atmospheric Stratification 

When the path is confined to a layer between receiver 
and transmitter, there are two limiting paths, as illus- 
trated in Figure 6A : Path A leaving the transmitter 
at some angle < 0 and arriving at the receiver with 
a = 0; Path B leaving the transmitter at an angle 

— 0 and arriving at the receiver with a > 0. By 
applying the equations deduced from theory and ex- 
pressed by data in Table 1, the necessary and sufficient 


Table 1 


Path 

a at 
receiver 
(degrees) 

jS at 

transmitter 

(degrees) 

Deviation 
of a and /3 
from true 
bearing 

Tn 

A 

0 

- 0.125 

+ 0.111 

0.64 

Intervening path 

+ 0.0625 

- 0.0625 

+ 0.1735 

1.00 

B 

+ 0.125 

0 

+ 0.236 

1.36 


modified refractive index distributions with height in 
the layer can be evaluated for the limiting paths A 
and B and for all intervening paths. Table 2 shows the 
value of the stratification parameter m required. We 
therefore conclude that, for a path confined to the 
layer between transmitter and receiver, the deviation 
from true bearing must be confined to the interval 
-J-0.111 to -j-0.236°, and the change in the modified 


ANALYSIS OF ANGLE-OF-ARRIVAL MEASUREMENTS 


209 


A 



B 



C 



Figure 6. Types of vertical variation in ray paths. 

refractive index between receiver and transmitter 
must be in range — 2 A to -|-2.4 M units. These 
limits hold for an approximately linear variation of 
index between receiver and transmitter. 

Eadiation along paths of type C, which penetrates 
the layer below the receiver height (see Figure 6B), 
arrives at the receiver at an angle a < 0 ; therefore, M 
will of necessity increase by more than 2.4 units from 
receiver to transmitter. We consider three stratifica- 
tions producing paths of this category. 

1. The so-called ^‘standard’^ atmosphere utilized 
for the purposes of representing ‘‘^normaT^ propagation 
by rectilinear rays on an earth distorted to a radius 
4/3 that of the true earth. The increase of M is at a 
rate of 3.6 units per 100 ft. 

2. Adiabatic equilibrium for an unsaturated at- 
mospheric layer, representing the condition of a com- 
pletely stirred or mixed stratum of air. The increase 
of M is 4.0 units per 100 ft. 

3. Eectilinear propagation on a true earth. For this 
condition there is no variation of electromagnetic 


velocity with height, and M increases by 4.76 units 
per 100 ft, equal to the rate of curvature of the earth. 

The computed deviations of the angles a and /3 at 
the receiver and transmitter, respectively, are given in 
Table 2. It will be noted that the condition of recti- 
linear propagation on a true earth produces an angle 

Table 2 


Deviation 


Type of 
atmospheric 
stratification 

a at 
receiver 
(degrees) 

jS at 

transmitter 

(degrees) 

of a and /8 
from true 
bearing 

m 

“Standard” 

atmosphere 

- 0.069 

- 0.194 

4- 0.042 

2.44 

Adiabatic 

equilibrium 

- 0.083 

- 0.208 

+ 0.028 

0.16 

Rectilinear 
propagation on 
a true earth 

- 0.111 

- 0.236 

0 

0 


a = — 0.11°, which is the true bearing from receiver 
to transmitter. From the data of Table 1 it follows 
that a ^‘^standard” atmosphere and an atmosphere 
vertically mixed so as to be in adiabatic equilibrium 
both provide a variation of modified refractive index 
with height of a magnitude such that the angle of 
arrival measured at the Beer’s Hill receiver under 
these conditions is within 0.04° of true geometric 
bearing. In view of the fact that the instrumental ac- 
curacy of the Beer’s Hill antenna system is ±0.04°, 
it follows further that the differences among these 
three meteorological stratifications will not be evident 
in the measurements. 

Consider now a case in which the radiation path 
penetrates the layer above the transmitter. The oc- 
currence of an angle of arrival at the Beer’s Hill re- 
ceiver in excess of 0.236° above true bearing will re- 
quire a path of propagation rising to some level above 
the New York City transmitter. The variation of M 
with height within the layer immediately above the 
transmitter will be critical in determining the magni- 
tude of the signal received and its angle of arrival. 
The analysis following is limited to one particular 
case of this category producing an extreme deviation 
from true bearing in the angle of arrival. 

For the paths shown in Figure 6C, the M distribu- 
tion between 353 and 492 ft above mean sea level is 
that computed from the observed meteorological data 
on the 400-ft tower at 0800 on July 7, 1944. Using 
only this portion of the actual sounding, the variation 
of modified index of refraction in the layer immedi- 
ately above the transmitter has been computed as a 


210 


ANGLE-OF-ARRIVAL EXPERIMENTS 


function of the angle a at the receiver. In the case of 
the angle a = 0.355° (deviation from true bearing 
equal to -|-0.466°), the calculated index at the level 
of total refraction, which computes as 505 ft, is very 
closely that observed at the uppermost level of mete- 
orological sounding (503 ft). Thus an angle of ar- 
rival deviating by as much as 0.47° from true geo- 
metric bearing is entirely possible for the meteoro- 
logical situation of 0800, July 7, 1944 and for the 
positions of the New York transmitter and Beer’s 
Hill receiver and could have been predicted from the 
observed meteorological sounding. 

A second significant conclusion can be readily de- 
duced by considering the modified refractive index 
distributions required in the layer immediately above 
the transmitter for different values of a. It is ap- 
parent that the lapse of modified index required for 
any of the angles considered in this example is not 
substantially different among all four angles; the 
primary requisite for the larger a’s is that the lapse 
continue to greater heights. Thus relatively small 
fluctuations in the meteorological elements can cause 
a time change of 0.1° in the angle of arrival measured 
at the Beer’s Hill receiver. Furthermore, a particu- 
larly unfavorable combination of small changes in the 
meteorological elements in this layer may cause the 
signal at the receiver to fall to a very low level. A 
similar conclusion is not valid for the case of propaga- 
tion confined to the layer between transmitter and re- 
ceiver and the case of path penetration below the re^* 
ceiver, since another slightly different path can al- 
ways be found along which energy can reach the re- 
ceiver directly. 

A third significant conclusion can be deduced by 
inspecting the computed deviations from true bear- 
ing of the angles at the receiver and the transmitter, 
as given in Table 3. It will be noted that the devia- 
tion from true bearing of the angle of arrival at the 
receiver is not the same as the deviation from true 
bearing of the angle of departure at the transmitter. 
In fact the data of Table 3 indicate that, under the 


Table 3 


a at 

jS at 

Deviation from 


receiver 

transmitter 

true bearing 


(degrees) 

(degrees) 

a 

|S 

m 

+ 0.355 

0.038 

+ 0.466 

-h 0.274 

1.366 

+ 0.372 

+ 0.119 

0.483 

-h 0.354 

1.972 

+ 0.401 

+ 0.190 

-h 0.512 

+ 0.426 

2.436 

+ 0.458 

+ 0.292 

q- 0.569 

+ 0.528 

3.052 



Figure 7. Correlation of deviations. 


meteorological situation of 0800 on July 7, 1944, the 
angle of arrival at the receiver would have been 
-|-0.27° above true bearing in place of -[-0.46°, were 
the receiver and transmitter interchanged at the end 
points of the path. On the other hand, for both cases 
1 and 2 treated above, the meteorological stratification 
was such that the angular deviations from true bear- 
ing at both receiver and transmitter were the same. 
The relations of the angular deviations from true 
bearing at the end points of the path are summarized 
in Figure 7. 

A fourth conclusion can be deduced by considering 
the curve in Figure 7 based on the computations tab- 
ulated in Table 3. It will be recalled that a fluctuation 
of 0.1° in angle of arrival at the receiver was con- 
cluded as possible as a result of relatively small fluc- 
tuations in the meteorological elements in the layer 
immediately above the transmitter. But it should now 
be noted that fluctuation of angle of departure at the 
New York transmitter is approximately 0.25° when 
the Beer’s Hill angle of arrival varies approximately 
0.1° for the particular meteorological situation of 
0800 on July 7, 1944. 

It therefore follows, in summary, that the deviation 
from true bearing measured at the position of the re- 
ceiver depends not only on the range between trans- 
mitter and receiver and on the meteorological condi- 
tions but also and equally well on the relative differ- 
ence in heights of transmitter and receiver and the 
position in height of the receiver with respect to the 
transmitter. 


ANALYSIS OF ANGLE-OF-ARRIVAL MEASUREMENTS 


211 


13.2.3 Comparison of Computed to 
Measured Angle of Arrival 

The experiiiieiital iiicasureiiieiits of angle of ar- 
rival secured 1)}^ Bell Telephone Laboratories and the 
meteorological data obtained on the 400-ft tower in 
Oakhnrsi, have been analyzed to determine whether 
any significant correlations exist between the meas- 
ured angles of arrival at the Beer’s Hill receiver and 
the angles of arrival computed from meteorological 
•data. A grand synthesis is presented in Figure 8 of 


all days for wind'll both BTL propagation measure- 
ments and Signal (Arps tower meteorological sound- 
ings were available for comparison. Since simultaneity 
in radio and meteorological measurements was a rare 
occurrence, the angle of arrival evaluations from both 
sources of data are plotted along a time scale (in 
hours) for each day of the period. The angle evalua- 
tions from radio data are represented by circles ; 
angles calculated from the meteorological data are 
represented by crosses of time length equal to the 
duration of sampling of the layer between transmitter 


HUNDREDTHS OF DEGREE 


HUNDREDTHS OF DEGREE 


HUNDREDTHS OF DEGREE 


-20 -10 0 10 20 30 40 


> 10 
3 ‘2 
Z 

16 

18 


'2 
? 14 

lO 16 


12 
14 
J 16 
^ 18 
(O 20 
22 
24 
2 
4 
6 

^ 8 
1 ^ 10 
12 
14 
16 


0 

2 

^ 6 

8 

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12 
14 


- 

T 

O 






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NO MEASUREMENT OF 
ANGLE OF ARRIVAL 



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REF 

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BTL 

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LEGEND 

RADIO MEASUREMENT 
JURACY +.04®) 

LE AT BEER'S HILL 
IPUTED FROM METEOR - " 
GICAL SOUNDING ON 
l-FOOT TOWER , 

HURST, NJ 

^L SOLID LINE AT -.11* 
ENTS TRUE GEOMETRIC _ 
; FROM BEER’S HILL 
iR TO NEW YORK 

FITTER 

1 1 1 1 1 1 


Figure 8. Measured ver.sus computed angles of arrival. 


212 


ANGLE-OF-ARRIVAL EXPERIMENTS 


and receiver (including both ascent and descent of 
the tower). Equipment limitations set the accuracy 
of BTL angle of arrival measurements at dzO.OT°. 

It is believed that generalized, overall conclusions 
for the entire period of comparison can be made as 
follows : 

1. That occasions of true bearing and ^^near true 
bearing” (say — 0.11 to 0°) could have been pre- 
dicted from the meteorological data. 

2. That the occurrence of extreme deviations from 
true bearing would have been predicted from mete- 
orological data nearest in time to the radio measure- 
ments. 

3. That the magnitude of the most extreme meas- 
ured deviation (0.46°) from true bearing can also be 
calculated from observed meteorological data, though 
not simultaneously observed. 

Conclusions 

The propagation path of microwave radiation can 
be fairly well specified, given only a knowledge of the 
temperature and water vapor pressure distribution 
in the lower atmosphere and the positions in space of 
transmitter and receiver. The equations of motion of 
the propagation of the individual wave fronts have 
been written in a form such that the angles of de- 
parture from the transmitter and the angles of arrival 
at the receiver can be evaluated directly from the 


meteorological stratification. Application of the theory 
to certain angle-of-arrival radio propagation experi- 
ments conducted by Bell Telephone Laboratories dur- 
ing the summer of 1944 has resulted in the following 
conclusions : 

1. A surprisingly good correlation exists between 
angles of arrival computed from meteorological and 
survey data only and the angles of arrival deter- 
mined experimentally. 

2. The extreme deviations (0.46°) from rectilinear 
propagation measured experimentally by BTL are con-* 
firmed as plausible on the basis of observed meteoro- 
logical stratification. 

3. The meteorological analysis indicates that de- 
viations from rectilinear propagation and the fluctua- 
tion of the deviations about a mean value are as much 
a function of position of transmitter and receiver 
as they are a function of the existing meteorological 
structure. 

It is strongly recommended that low-level meteoro- 
logical soundings be considered an indispensable part 
of any experimental angle-of-arrival measurements. 
The good correlations secured between evaluation of 
angles of arrival from meteorological data and angles 
of arrival measured experimentally suggest that de- 
viations from rectilinear propagation can be ac- 
counted for by measurable atmospheric conditions 
and that, further, these deviations can be reasonably 
well predicted. 


BIBLIOGRAPHY^ 


Xiinibers such as CP-31 1 -j\I 4 indicate that the document listed has been microfilmed and that its title appears in 
the microfilm index })rinted in a separate volume. For access to the index volume and to the microfilm, consult the 
Army or Navy agency listed on the reverse of the half-title page. 


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1 . Microwave Transmission over Water and Land under 
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1. Transmission of Plane IFares Through a Single Stratum 
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Chapter 3 

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5. Reviews of Progress of Ultra. Short Wave Propagation Work, 

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10. Reviews of Progress of Ultra Short W ave Propagation Work, 
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CP-llO-Mll 

11. Reviews of Progress of Ultra Short Wave Propagation W ork. 

Part XI, Study of Reflection Coefficient of the Sea at Centi- 
meter Wavelengths, F. Hoyle, OSRD WA-3157-2, Report 
AC-7027, USWP, Oct. 14, 1944. CP-110-M12 

12. Reviews of Progress of Ultra Short Wave Propagation Work, 

Part XII, Some K-, X-, and S-Band {Llandudno) Trials, 
General Summary of the Experimental Results Obtained 
which are Concerned with the Dependence of Radio Propa- 
gation on Meteorological Conditions, OSRD WA-3 157-3, 
Report AC-7028, TRE and RRDE Report, USWP, 
Oct. 14, 1944. CP-110-M13 

13. Reviews of Progress of Ultra Short Wave Propagation Work, 

Part XIII, Progress Report on 369 Trials by DNMS, 
OSRD WA-3156-1, Report AC-7029, USWP, Oct. 14, 
1944. CP-110-M14 

14. Reviews of Progress of Ultra Short W ave Propagation W ork, 
Part XIV , Survey of Progress in the United Kingdom on the 
Electromagnetic Theory of Tropospheric Propagation, OSRD 


213 


214 


BIBLIOGRAPHY 


WA-3157-4, Report AC-7030, RRDE-USWP, Oct. IG, 
1944. CP-110-M15 

15. Reviews of Progress of Ultra Short Wave Propagation Work, 
Part XV, Study of Meteorological Factors Responsible for 
the Refractive Structure of the Troposphere, OSRD WA- 
3157-5, Report AC-7031, RRDE-USWP, Oct. 16, 1944. 

CP-110-M16 

16. Centimeter Wave Propagation over Land, Preliminary Study 
of the Field Strength Records Between March and Sept., 1943, 
R. L. Smith-Rose and A. C. Stickland, OSRD WA-1514-6, 
Report RRB/S-13, DSIR, Nov. 15, 1943. CP-333-M1 

17. Centimeter Propagation over Land, A Study of the Field 
Strength Records Obtained During the Year 1 943-1 944i 
Report RRB/S-18, NPL-MO DSIR, May 11, 1944. 

CP-224-M11 

Chapter 6 

1. Beitraege zur Physik der Freien Atmosphere, P. Mildner, 
1932, p. 51. 

2. Geophysical Memoirs, Giblett and others, No. 54. 

3. Proceedings of the Royal Society of London, O. G. Sutton, 
1932, p. 143. 

4. Geophysical Memoirs, No. 65. 

5. Quarterly Journal of the Royal Meteorological Society, 
O. G. Sutton, 1936, p. 125. 

6. Quarterly Journal of the Royal Meteorological Society, 
H. V. Sverdrup, 1936, p. 461. 

7. MIT Papers, Rossby and Montgomery, 1934. 

8. Quarterly Journal of the Royal Meteorological Society, 
O. G. Sutton, 1937, p. 105. 

9. Wired Sonde Equipment for High Altitude Soundings, 

Lloyd J. Anderson, BuShips Problem X4-49CD, Report 
WP-16, NRSL, Nov. 17, 1944. CP-341-M2 

10. The Captive Radiosonde and Wired Sonde Techniques for 

Detailed Low-Level Meteorological Sounding, Paul A. 
Anderson, C. L. Barker, K. E. Fitzsimmons, and S. T. 
Stei)henson, OEMsr-728, Research Project PDRC-647, 
Division 14 Report 192, Report 3, Washington State 
College, Oct. 4, 1943. CP-341-M1 

11. The Dielectric Constant of Water Vapour and its Effect 

upon the Propagation of Very Short Waves, A. C. Stickland, 
OSRD WA-175-7, Paper RRB/S-2, NPL-DSIR, May 11, 
1942. CP-522. 12-M2 

12. Lehrbuch der Meteorologie, Funfte Auflage, J. Hann and 
R. Suring, 1939. 

13. “On Temperature and Humidity Observations Made at 
Allahabad,” S. A. Hill, Indian Meteorological Memoirs, 
4, Part 6, 1889. 

14. “Ein Beitrag zur Kenntnis der Temperatur und Feuchtig- 
keitsverhaltnisse in Verschiedener Hohe iiber dem Erd- 
boden,” K. Knoch, Verbffentlichungen des Koniglichen 
Preussischen, Meteorologischen Institute, Abhandlungen, 
.3, No. 2, 1909. 

15. “An Investigation of the Lap.se Rate of Temperature in 
the Lowest Hundred Meters of the Atmosphere,” N. K. 
Johnson and G. S. P. Heywood, Geophysical Memoirs, 
No. 77, 1938. 

16. Walter M. Elsasser, NDRC Propagation Memorandum. 

17. Atmospheric Waves, Fluctuations in High Frequency Radio 
Waves, L. G. Trolese and .John B. Smyth, BuShips Prob- 
lem X4-49CD, Report WP-18, NRSL, Feb. 1, 1945. 

CP-225-M1 


18. Dynamic Meteorology, Bernhard Haurwitz, McGraw-Hill 
Book Co., 1941. 

18a. Ibid., p. 286. 

\%h.Ibid., p. 288. 

19. Meieorologische Zeitschrift, Bernhard Haurwitz, 1931. 

20. Monthly Weather Review, W. C. Jacobs, 65, No. 9, 1947. 

21. “Microbarometric Oscillations at Blue Hill,” Bernhard 
Haurwitz, R. Stone, and C. F. Brooks, Bulletin of the 
Atnerican Meteorological Society, 16, Nos. 6-7, 1935, 
pp. 153-159. 

22. Wissenschaftliche Ergebnesse der Deutschen Atlantischen 
Expedition auf dem Forschungs-und Vermessungsschiff, 
Meteor, 1925-1927, 15, Berlin Leipsig, 1933. 

23 . Q ualitative S urvey of M eteorological Factors Affecting M icro- 
wave Propagaiion, 1. Katz and J. M. Austin, OEMsr-262, 
Division 14 Report 488, RL, June 1, 1944. CP-31 1-M3 

24. “Die Passatinversion,” von Ficker, Veroffentlichungen 
des Meteorologischen Instituts der Universitdt, Berlin, 1, 
No. 3, 1936. 

25. Modified Index Distribution Close to the Ocean Surface, 
R. B. Montgomery and Robert H. Burgoyne, OEMsr-262, 
Division 14 Report 651, RL, Feb. 16, 1945. CP-222.2-M1 

26. Results of Low Level Atmospheric Soundings in the South- 
west and Central Pacific Ocean Areas, Paul A. Anderson, 
K. E. Fitzsimmons, G. M. Grover, and S. T. Stephenson, 
OEMsr-728, Research Project PDRC-647, NDRC Report 
9, Washington State College, Feb. 27, 1945. CP-335-M4 

27. Atlas of Climatic Charts of the Oceans, W. F. McDonald, 
U. S. Dept, of Agriculture, Weather Bureau, 1938. 

28. Atmospheric Refraction, A Preliminary Qualitative Inves- 
tigation, Lloyd J. Anderson, F. P. Dane, J. P. Day, R. F. 
Hopkins, L. G. Trolese, and A. P. D. Stokes, BuShips 
Problem X4-49CD, Report WP-17, NRSL, Dec. 28, 1944. 

CP-222-M9 


Cliapler 7 

1. Bureau of Standards Journal of Research, Diamond, 
Hinman, F. W. Dunmore, and Lai)ham. 25, 1940, p. 328. 

2. Bureau of Standards Journal of Research, D. N. Craig, 
21, 1938, p. 225. 

3. Bureau of Standards Journal of Research, F. W. Dunmore, 
23, 1939, p. 702. 

4. Instruments and Methods for Measuring Temperature and 

Humidity in the Lower Atmosphere, I. Katz, OEIMsr-262, 
Service Project SC-8, Division 14 Report 487, RL, 
Apr. 12, 1944. CP-344-M2 

5. The Captive Radiosonde and Wired Sonde Techniques for 

Detailed Low-Level Meteorological Sounding, Paul A. 
Anderson, C. L. Barker, K. E. Fitzsimmons, and S. T. 
Stejihenson, OEMsr-728, Research Project PDRC-647, 
Division 14 Report 192, Report 3, Washington State 
College, Oct. 4, 1943. CP-341-M1 

5a. Report of Second Propagation Conference, February 10 to 
11, 1944 at the Empire State Building, New York, OEMsr- 
1207, CUDWR-WPG, February 1944, p. 38. CP-100-M2 

bh. Notes on Operational Use of Low-Level Meteorological 
Sounding Equipment, K. E. Fitzsimmons, S. T. Stephen- 
son, and Robert W. Bauchman, OEMsr-728, Research 
Project PDRC-647, Report 7, Washington State College, 
June 15, 1944. CP-342-M2 

Operating Instructions for the WSC Low-Level Atmospheric 
Sounding Equipment, Paul A. Anderson, OEMsr-728, 


BIBLIOGRAPHY 


215 


Ilcfsearch Project PDRC-647, Rci)ort 8, Washington State 
College, July 10, 1944. CP-342-M3 

G. Journal of Scientific Inslrumcnts, P. A. Sliei)pard, 17, 1940, 

p. 218. 

7. A Remote Indicating Cup Anemometer with Magnetic 
Coupling, Roscoe G, Dickinson and Douglas L. Kraus, 
OSRD 3714, NDCrc-137 and OEMsr-861, Service Project 
CWS-26, NDRC Division 10, CIT, Apr. 10, 1944. 

Div. 10-30 1.1-M2 

8. Geophysical Memoirs, N. K. Johnson, No. 46, 1929. 

9. Propagation and Reflection Characteristics of Radio Waves 

as Affecting Radar, W. G. Michels and W. C. Pomeroy, 
Service Project (M-3) 11a, U.S. Army Air Forces Board, 
Orlando, Fla., Jan. 31, 1944. CP-531-M1 

10. Balloon Psychrometer for the Measurement of the Relative 

Humidity of the Atmosphere at Various Heights (and 
Addendum), S. M. Doble and S. Inglefield, OSRD 11-5- 
5079(S) and OSRD lI-5-5080(S), ICI, Apr. 1, 1943; 
Addendum Sept. 25, 1943. CP-344-M1 

11. Report of Friez Instrument Division Bendix Aviation Corp., 

to the Bureau of Ships, May 1944. CP-342-M1 

Chapter 8 

1. K-Band Rain and Water-Vapor Attenuation over Tokyo, 
Arthur E. Bent and E. IM. Purcell, Division 14 Report, RL. 

2. Modified Index Distribution Close to the Ocean Surface, 
R. B. Montgomery and Robert H. Burgoyne, OEMsr-262, 
Division 14 Report 651, RL, Feb. 16, 1945. 

CP-222.2-M1 

3. Determination of a Suitable Method of Forecasting Radar 

Propagation Variations over Water, Tests Conducted by 
26th Weather Regidn, Orlando, Florida, J. R. Gerhardt 
and William E. Gordon, Service Project 4252R000.77, 
U. S. Army Air Forces, Mar. 10, 1945. CP-425-M1 

4. Tropospheric Propagation and Radio Meteorology, Report 
WPG-5, CUDWR-WPG, September 1944. 

5. Preliminary Instruction Manual, Weather Forecasting for 

Radar Operations, Report 614, U. S. Army Air Forces, 
Weather Division, March 1944. CP-410-M4 

6. Variations in Radar Coverage, Report JANP-101, Joint 

Communications Board June 1, 1944. CP-202.4-M4 

Earlier edition: IRPL T-1, CUDWR-WPG, May 1944. 

CP-202.5-M1 

7. Tropospheric Weather Factors Likely to Affect Super-refrac- 

tion of VHF-SHF Radio Propagation as Applied to the 
Tropical West Pacific, E. Dillon Smith and R. D. Fletcher, 
Report RP-1, U. S. Department of Commerce, Weather 
Bureau, July 1, 1944. CP-424-M1 

8. Nomograms for Computation of Alodified Index of Refrac- 

tion, Robert H. Burgoyne, OEMsr-262, Division 14 
Report 551, RL, Apr. 6, 1945. CP-222. 1-M7 

9. Tables for Computing the Modified Index of Refraction M, 
E. R. Wicher, Report WPG-8, CUDWR, March 1945. 

10. Elements of Radio Meteorological Forecasting, H. G. 

Booker, Report T-1621, Mathematics Group, TRE, 
Malvern, Feb. 14, 1944. CP-410-M3 

11. World Atlas of Sea Surface Temperatures, Hydrographic 
Office, No. 225, 1944. 

12. Atlas of Climatic Charts of the Oceans, P. W. Kenworthy, 
U. S. Weather Bureau, 1938. 

13. Monthly Meteorological Chavis of the W esteVn Pacific Ocean, 
Marine Branch of the Meteorological Office, British Air 


Ministry, London, England. 

14. Climatic Atlas of Japan and Her Neighboring Countries, 
United States Navy Reprint, 1943. 

15. Climatic Atlas for Alaska, Report 444, Weather Bureau 
Information Branch, Headquarters Army Air Forces. 

16. Third Conference on Propagation, Washington, D. C. [on] 

November 16 to IS, 1944, NDRC CUDWR-WPG, 1945, 
pp. 5-6. CP-100-M4 

17. Effect of Meteorological Conditions at Saipan upon Radar 
Coverage, JEIA Survey Report 8888, Dec. 5, 1944. 

18. Results of Low Level Atmospheric Soundings in the South- 

west and Central Pacific Oceanic Areas, Paul A. Anderson, 
K. E. Fitzsimmons, G. M. Grover, and S. T. Stephenson, 
OEMsr-728, Research Project PDRC-647, Report 9, 
Washington State College, Feb. 27, 1945. CP-335-M4 

19. Preliminary Instruction Manual of Weather Forecasting 

for Radar Operations in South West Pacific Areas, D. F. 
Martyn and P. Squires, Report RP-220, CSIR-RL, 
Sept. 4, 1944, p. 46. CP-424-M2 

20. The Air Defense System of the Near Islands, Thomas J. 

Carroll, Report OAD-55, U. S. Army Air Forces, Eleventh 
Air Force, OCSO, Operational Analysis Division, Aug. 
30, 1944. CP-202. 1-M5 

21. The Coincidence of Temperature Inversions and Non- 
Standard Radar Propagation and Reflection, Report JEIA 
8366. 

Chapter 9 

1. Interim Report on Experiments on Ground Reflection at a 
Wavelength of 9 Cm, L. H. Ford, RRB/C-101 or JEIA 
4899, DSIR, July 7, 1944. 

2. An Experimental Investigation of the Reflection and Ab- 

sorption of Radiation oj 9-Cm Wavelength, L. H. Ford and 
R. Oliver, OSRD WA-3386-2, Report RRB/C-107, 
DSIR, Oct. 27, 1944. CP-532-M2 

3. S-Band Measuremerds of Reflection Coefficietds for Various 

Types of Earth, E. M. Sherwood, Report 5220.129, Sperry 
Gyroscope Company, Oct. 29, 1943. CP-532. 1-Ml 

4. CentBneter Wave Propagation over Sea within the Optical 

Range, H. Archer-Thomson, J. C. Dix, F. Hoyle, E. C. S. 
Megaw, and M. H. L. Pryce, OSRD W-157-16, Report 
M-398, ASE, January 1942. CP-532.2-M1 

5. Preliminary Report on the Reflection of 9-Cm Radiation 

at the Surface of the Sea, H. Archer-Thomson, N. Brooke, 
T. Gold, and F. Hoyle, OSRD WA-1 131-2, Report M-532, 
ASE, September 1943. CP-532.2-M2 

6. PrelimBiary Measurements of 10-Cm Reflection Coefflcierds 

of Land and Sea at Small Grazing A7igles, Pearl J. Ruben- 
stein and William T. Fishback, Division 14 Report 478, 
RL, Dec. 11, 1943. CP-532-M1 

7. Further Measurements of 3- and lO-Crn Reflection Coeffi- 

cients of Sea Water at Small Grazing Angles, William T. 
Fishback and Pearl J. Rubenstein, OEMsr-262, Division 
14 Report 568, RL, May 17, 1944. CP-532.2-M4 

8. Ground Reflection Coefficient Experiments on X-Band, 

Case 20564, W. M. Sharpless, Report MM-44-160-250, 
BTL, Dec. 15, 1944. CP-532.1-M3 

9. Scattering, R. L. Eckersley, OSRD WA-2255-lf, JEIA 
3904, Report TR-481, BRL, November 1943. CP-512-M3 

10. Reflection and Scattering, T. L. Eckersley, OSRD WA- 
4002-12, Report TR-506, BRL, January 1945. 

CP-532.2-M5 


216 


BIBLIOGRAPHY 


Chapter 10 

1. TJie Atmospheric Absorption of Microwaves (in Third 

Conference Report of CP), J. H. Van Vleck, Report 175 
(43-2), RL, Apr. 27, 1942. Div. 14-121. 1-M4 

See also Third Conference, Nov. 16-18, 1944. CP-100-M4 

2. Further Theoretical Investigations on the Atmospheric Ab- 

sorption of Microwaves, J. H. Van Vleck, OEMsr-262, 
Service Project AN-25, Division 14 Report 664, RL, 
Mar. 1, 1945. CP-510-M8 

3. Propagation of K/2 Band Waves, G. E. Mueller, Report 

MM-44-160-150, BTL, July 3, 1944. CP-511-M7 

4. The Absorption of One-Half Centimeter Electromagnetic 
ITat’CS in Oxygen, E. R. Beringer, OEMsr-262, Service 
Project AN-25, Division 14 Report 684, RL, Jan. 26, 1945. 

CP-510-M7 

5. The Absorption of Atmospheric Water-Vapor in the K-Band 
Region, R. H. Dicke, R. L. Kyhl, A. B. Vane, and E. R. 
Beringer, Division 14 Report 1002, RL, Jan. 15, 1946. 

Div. 14-122. 13-M5 

6. An Aerial Investigation of K-Band Radar Performance 

under Tropical Atmospheric Conditions, R. S. Bender, 
A. E. Bent, and J. W. Miller, Division 14 Report 729, 
RL, Oct. 1, 1945. Div. 14-122.23-M6 

7. Rotational Line Width in the Absorption Spectrum of 

Atmospheric Water Vapor and Supplement, Arthur Adel, 
OEMsr-1361, NDRC Division 14 Report 320, L^niversity 
of Michigan, Oct. 10, 1944; Supplement Feb. 1, 1945. 
(see also reference 2) CP-510-I\I6 

8. Annalen der Hydrographic, AI. Diem, Berlin, 70, 1942, 
pp. 142-150. 

9. An Investigation on the Number and Size Distribution of 
Water Particles in Nature, Josef Mazur, F/Lt. Polish Air 
Force, OSRD 11-5-6306(8), Report MRP-109, Meteoro- 
logical Research Committee, Great Britain, June 10, 1943. 

CP-51 1-M5 

10a. Provincetown Path, private communication from Donald 
E. Kerr and G. T. Rado of RL. 

10b. Measurements of the Attenuation of K-Band Waves by Rain, 
G. T. Rado, OEMsr-262, Service Project AN-25, Division 
14 Report 603, RL, Mar. 7, 1945. CP-51 1-M 10 

11. Interim Report of the U. S. W. Panel Workivig Committee, 
Part I, Water in the Atmosphere, A. C. Best, JEIA 7607, 
Report AC-7375, MO-USW, Aug. 14, 1944. 

12. Interim Report of the U. S. W. Panel Working Committee, 
Part III, Attenuation of Centimeter Waves by Rain, Hail, 
and Cloiids, J. W. Ryde and D. Ryde, JEIA 7607, Report 
AC-7375, USWP, Report 8516, GEC, Aug. 3, 1944. 

13. Polar Molecules, P. Debye, The Chemical Catalogue Co., 
New YMrk, 1929. 

14. Summer Storm Echoes on Radar MEW, J. S. Marshall, 

R. C. Langille, William M. Palmer, R. A. Rodgers, G. P. 
Adamson, and F. F. Knowles, Report 18, CAORG, 
Nov. 27, 1944. CP-621. 1-M2 

15. The Effect of Clutter Fluctuations on MTI, H. Goldstein, 
Division 14 Report 700, RL, Dec. 27, 1945. 

Div. 14-263. 1-M4 

16. Annalen der Physik, G. Mie, 25, 1908, p.377. 

17. Echo Intensities and Attenuation Due to Clouds, Rain, 

Hail, Sand, and Dustslorms at Centimeter Wavelengths, 
J. W. Ryde, OSRD WA-81-25, Report 7831, GEC, 
Oct. 13, 1941. CP-511-M1 

18. Electromagnetic Theory, J. A. Stratton, McGraw-Hill 
Book Co., 1941. 


18a. Ibid., i)p. 563-573. 

ISh. Ibid., pp. 554-560. 

19. The Theory of Sound, Lord Rayleigh, McIMillan and Co., 
Ltd., London, 1940. 

20. On Light Scattering by Spheres, Parts I and II, Leon 
Brillouin, OEMsr-1007, AMG-C 100 and 132, AMP 87.1 
and 87.2, December 1943 and Ai)ril 1944. 

AIVIP-202-M2, M3 

21. Preliminary Report on the Dielectric Properties of Water 
in the K-Band, C. H. Collie, CL Misc. 25, CVD Rejjort, 
May 1944. 

22. Properties of Ordinary Water-Substance, N. E. Dorsey, 
American Chemical Society Monograph Series, Reinhold 
Publishing Corp., New York, pp. 350-373. 

23. Dielectric Properties of Water and Ice at K-Band, E. L. 

AMunker, OEMsr-262, Service Project AN-25, Division 
14 Report 644, RL, Dec. 4, 1944. CP-522. 1-M2 

24. H. G. Houghton’’ s data reproduced in: Aeronautical Meteor- 
ology, G. F. Taylor, Pitman Publishing Corp., New YMrk- 
Chicago, 1943. 

25. Physics of the Air, W. J. Humphreys, McGraw-Hill Book 
Co., 1940. 

26a. Third Conference on Propagation, Washington, D. C. [on] 
November 16 to 18, 1944) E- Dillon Smith, NDRC 
CUDWR-WPG, 1945. CP-100-M4 

26b. J. O. Laws and D. O. Parsons, National Research Council, 
Transactions of the American Geophysical Union, Part II 
1943, p. 452. 

27. The Effect of Rain upon the Propagation of l-Cm Electro- 

Magnetic Waves, Case 22098, S. D. Robertson, Report 
IMM-42-160-87, BTL, Aug. 1, 1942. CP-51 1-M2 

28. Absorption of 1-Cm Radiation by Rain, M. G. Adam, R. A. 
Hull, and C. Hurst, Misc. Report 3, CVD-CL. 

29. K-Band Radar Transmission, A Preliminary Report of 

Tests Made Near Atlantic Highlands, N. J. between 
December 1943 and April 1944) G. C. Southworth, A. P. 
King, and S. D. Robertson, Report ]\IM-44-160-115, 
BTL, May 19, 1944. CP-202.2-1M1 

30. The Effect of Rain on the Propagation of Microwaves, 

Case 22098, A. P. King and S. D. Robertson, Report 
MM-42-160-93, BTL, Aug. 26, 1942. CP-51 1-M3 

31. Calibration and Operational Tests of AN/CPS-L {AIEW), 
Army Air Forces Board Project (M-3)-9, Mar. 30, 1944. 

32. Radar Echoes fro7n Atmospheric Phenomena, A. E. Bent, 
Division 14 Report 173(42-2), RL, Mar. 13, 1943. 

CP-621.1-M1 

33. A. E. Bent, RL, unpublished report, Feb. 29, 1944. 

34. Radar Eehoes from Clouds of Water Droplets, F. Hoyle, 
Report AC-7930, USW 128, Mar. 16, 1945. 

35. A. J. F. Siegert, RL unpublished, 1943. 

36. Interim Report of the C/.S.IF. Panel Working Comtnittee, 
Part II, The Attenuation of Centimeter Waves by Atmos- 
pheric Gases, J. M. Hough, JEIA 7607, Report AC-7375, 
USW, July, 1944. 

37. Interim Report on Experiments on Ground Reflection at a 
Wavelength of 9 Cm, L. H. Ford, JEIA 4899, Report 
RRB/C-lOl, DSIR, July 7, 1944. 

38. The Dielectric Properties of Water in the Temperature 
Range 0° C to 40° C for Wavelengths of 1.24 Cm 1.58 
Cm, J. A. Saxton and J. A. Lane, JEIA 9811, Report 
RRB/C-116, DSIR, Mar. 7, 1945. 

39. The Anomalous Dispersiovi of Water at Very High Radio 
Frequencies in the Temperature Range 0° C to 40° C, 


BIBLIOGRAPHY 


217 


J. A.Saxton, JEIA 9812, Report RRB/C-118, NPL-DSIR, 
Apr. 6, 1945. CP-522. 11-M3 

40. A New Method for Measuring Dielectric Constant and Loss 

in the Range of Centimeter Waves, S. Roberts and Arthur R. 
von Hippel; Wave Guides with Dielectric Sections, L. J. 
Chu, Report 102, MIT, March 1941. CP-521-M1 

41. The Measurement of Dielectric Constant and Loss with 

Standing Waves in Coaxial Wave Guides, Arthur R. von 
Hippel, D. G. Jelatis, and W. B. Westphal, OEMsr-191, 
NDRC Division 14 Report 142, Laboratory for Insulation 
Research, MIT, April 1943. CP-521-M4 

42. Auxiliary Equipment for the MIT Coax Instrument and 

Its Use, Arthur R. von Hippel, D. G. Jelatis, W. B. 
Westphal, M. G. Haugen, and R. E. Charles, OEMsr-191, 
NDRC Division 14 Report 210, Laboratory for Insulation 
Research, MIT, Nov. 1, 1943. Div. 14-131.2-Ml 

43. T. A. Taylor and Willis Jackson, Ministry of Supply, 
CPR Report 30. 

44. “The Dielectric Dispersion and Absorption of Water and 
Some Organic Liquids,” W. P. Connor and C. P. Smyth, 
Journal American Chemical Society, 65, 1943, pp. 382-389. 

45. Progress Report on Ultra High Frequency Dielectrics, 

Arthur R. von Hippel, OEMsr-191, NDRC Division 14 
Report 121, Laboratory for Insulation Research, MIT, 
January 1943. CP-521-M2 

46. R. Dunsmuir and J. Lamb, Ministry of Supply, 287/ 
Gen/35, DSR Report 61, Department of Scientific Re- 
search, Mar. 5, 1945. 

47a. The Dielectric Constant and Absorption Coefficient of W ater 
Vapour for Wavelengths of 9 Cm and 3.2 Cin, Frequencies 
3,330 and 9,350 Mc/s, J. A. Saxton, Paper RRB/S-11, 


NPL-DSIR, June 14, 1943. CP-522.12-M3 

47b. The Dielectric Constant and Absorption Coefficient of Water 
Vapour for Radiation of Wavelength 1.6 Cm, Frequency 
18,800 Mc/s, J. A. Saxton, Report RRB/S-17, NPL- 
DSIR, Apr. 22, 1944. 

48. The Relation between Absorption and the Frequency De- 
pendence of Refraction (Fourth Conference), J. H. Van 
Vleck, Division 14 Report 735, RL, May 26, 1945. 

Div. 14-122.24-M4 


Chapter 12 

1. Possible Measurement of Radar Echoes by Use of Model 
Targets, S. A. Goudsmit and P. R. Weiss, Division 14 
Report 196 (43-24), RL, Mar. 4, 1943. 

Div. 14-122.113-M5 

2. The Theory of Random Processes, G. E. Uhlenbeck, Divi- 
sion 14 Report 454, RL, Oct. 15, 1943. Div. 14-125-M7 

3. On the Fluctuations in Signals Returned by Many Inde- 
pendently Moving Scatterers, A. J. F. Siegert, Division 14 
Report 465, RL, Nov. 12, 1943. Div. 14-122.113-M7 

Chapter 13 

1. Measurements of the Angle of Arrival of Microwaves in the 
X-Band, Case 20564, W. M. Sharpless, Report MM-44- 
160-249, BTL, Nov. 7, 1944. 

2. Ground Reflection Coefficient Experiments on X-Band, 

Case 20564, W. M. Sharpless, Report MM-44- 160-250, 
BTL, Dec. 15, 1944. CP-532.1-M3 




OSRD APPOINTEES 


COMMITTEE ON PROPAGATION 

Chairman 

Chas. R. Burrows 


H. II. Beverage 

Members 

Martin Katzin 

T. J. Carroll 

D. E. Kerr 

J. H. Dellinger 

J. A. Stratton 

S. S. Attwood 

Consultants 

C. E. Buell 


J. A. Stratton 

Technical Aides 

(Listed in the order they served.) 

A. F. Murray S. W. Thomas 


R. J. ITearon 



CONTRACT NUMBERS, CONTRACTORS, AND SUBJECTS OF CONTRACTS 


Contract No. 

Contractor 

Subject 

OEMsr-1207 

Columbia University- 

New York City, New York 

1 

Correlation, analysis and integration of data on 
radio and radar propagation. 

OEMsr-728 

State College of Washington 

Pullman, Washington 

Develop meteorological equipment and conduct 
meteorological soundings in the Southwest Pacific 
and correlate it with radio propagation data. 

OEMsr-1497 

Humble Oil & Refining Company 
Houston, Texas 

Development and construction of microwave field 
strength measuring sets. 

OEiMsr-1496 

University of Texas 

Austin, Texas 

Development of equipment for and making measure- 
ments of time and space deviations in radio 
wave propagation. 

OEMsr-1502 

Jam Handy Organization, Inc. 

Detroit, Michigan 

Preparation of a General Outline of Training 
Material and the preparation of manuals, films 
and other training aids for use in instructing 
technical and other personnel in radio-weather 
and radio propagation. 


221 


SERVICE PROJECT NUMBERS 


The Committee on Propagation did all of its work under 
Project Control SOS-9, which was originally set up through 
the request of the Combined Chiefs of Staff following recom- 
mendations submitted by the Combined Meteorological Com- 
mittee : 

1. That the Committee on Propagation of the National 
Defense Research Committee be requested to act as a co- 
ordinating agency for all meteorological information associated 
with short wave propagation; 

2. That the Committee on Propagation be requested to 
forward periodically to the CMC a list of all reports and 
papers dealing with the meteorological aspects on short wave 
propagation which have been received or transmitted by 
that -Committee. 

Later the Combined Meteorological Committee in its 37th 
meeting on Tuesday, February 22, 1944, agreed that the 
National Defense Research Committee (NDRC) Committee 
on Propagation be recognized as the supervising committee on 
all basic research being done in the United States on the 
related problems of radar propagation and weather, in addi- 
tion it shall be the recognized channel whereby international 
exchange of papers of the two related sciences will be effected. 

The Joint Communications Board therefore approved the 
following policy, which was concurred in by NDRC and by 
the Joint Meteorological Committee: 

1. The NDRC Propagation Committee and its associated 
working groups will initiate and exercise technical supervision 
over such tests and investigations as they deem necessary to 
ascertain the nature of the above-mentioned propagation 
anomalies in the VHF, UHF, and SHF bands, to devise the 
most practicable methods to determine the occurrence and 
characteristics of these anomalies from appropriate meteoro- 


logical forecasts, with a view to improving the interim solutions 
offered by the Joint Wave Propagation Committee of the JCB. 

2. The Army and Navy will furnish by direct coordination 
between them the basic staff guidance for such tests and 
investigations. They will accomplish this by determining: 

a. The specific forms in which basic prediction data 
shall be presented, and 

b. The method of use required for operational forecast 
of propagation anomalies in the VHF, UHF, and SHF bands. 

3. When the NDRC requires the cooperation of the operat- 
ing units of the Army and Navy in conducting such tests and 
investigations as it deems necessary and this cooperation is 
of such an extent and nature that it cannot be furnished by 
informal coordination, it will be requested through the Joint 
Wave Propagation Committee of the JCB. Such requests will 
be initiated by the NDRC representative on the Wave Propa- 
gation Committee and recommended to the Joint Communica- 
tions Board by the Joint Wave Propagation Committee for 
consideration. 

4. The Joint Wave Propagation Committee will be respon- 
sible for devising and furnishing immediately, interim opera- 
tional forecasting guides based upon information already 
available. 

On April 3, the Coordinator of Research and Development 
requested that the Army Project SOS-9 be made a joint Army- 
Navy project. Project No. AN-16 was assigned to this. 

On May 23, 1944, the Chief Signal Officer requested that 
under Project AN-16 the following work be inaugurated: 

Project AC 230.04 “Wave Propagation* Study of Line- 
of-Sight Communication and Navigation.” 


222 


INDEX 


The subject indexes of all STR volumes are combined in a master index printed in a separate volume. 
For access to the index volume coasult the Army or Navy Agency listed on the reverse of the half-title page. 


Absolute humidity, definition, 132 
Absorption by the atmosphere 
see Atmospheric absorption and scat- 
tering 

Absorption coefficient of spherical rain- 
drops, 157-158 

Absorption cross section of raindrops, 
157-158 

Adiabatic lapse rate, drv (definition), 
132-133 

Air, modification by sea surface, 124 
Air mass, definition, 132 
Aircraft cross sections 
effect of frequency, 203 
effect of type and dimensions of air- 
craft, 203 
effect of wind, 203 
Anemometers, 99-100 
Angle-of-arrival, 205-212 

comparison of measured and com- 
puted angle, 211 
deviation from true bearing, 210 
direct and reflected wave, 206 
effect of atmospheric stratification, 
208-210 

effect of rain, 206 

effective coefficient of reflection, 206 
horizontal, 206 
meteorological analysis, 207 
method of measurement, 205 
theory from meteorological point of 
view, 207 
vertical, 206 

vertical variations in ray i)aths, 209 
Angle-of-departure, 207 
Antenna height, effect on signal 
strength, 37-39, 44-45 
Antennas for S- and X-band trans- 
mission, 33-34 

Antigua radio wave transmission ex- 
periments, 33-46 

Arizona radio wave transmission ex- 
periments, 29-32 
Artificial echo, radar, 198 
A-scope, radar, 192, 198 
Atmosphere, standard (definition), 130 
Atmospheric absorption and scattering, 
148-186 

attenuation by idealized precipita- 
tion forms, 162-165 
attenuation by rain, 149, 157-159 
attenuation by spherical drops, 157- 
159 

attenuation due to water vapor, 185 
back scattering, 167-171 
British work, 180 
by clouds, fogs, rain, 159-162, 180 
by oxygen and vapor, 180 
by spherical particles, 150-154, 157- 
159 

dielectric constant of liquid water, 
180-185 


dielectric constant of steam, 185-186 
gaseous absorption, 148-151, 171 
K-band absorption by water vapor, 
175-177 

K-band attenuation by rainfall, 177- 
180 

scattering amplitudes, 154-157, 171 
scattering by spherical raindrops, 
165-167 

scattering variations with frequency, 
146 

technique for measuring attentuation 
in the atmosphere, 175 
Atmospheric refraction of radio waves 
see Refractive index and M curves 
Atmospheric stratification and angle- 
of-arrival, 208 
Attenuation 

see Atmospheric absorption and scat- 
tering 

Back scattering, 153-154, 167-171 
Balloon sondes, captive, 101-104 
cable and balloon techniques, 103-104 
radio transmission type, 101-102 
wired transmission type, 102-103 
Bell Telephone Laboratories (BTL), 
angle-of-arrival measurements, 
207 

Bermuda high-pressure area, 40 
Brillouin attenuation formulas for at- 
mospheric absorption, 154 
British radio transmission experiments, 
47-60 

atmospheric absorption of micro- 
waves, 180 

fading in line-of-sight, 58-59 
forecasting system based on tempera- 
ture gradient, 59-60 
objectives of study, 47 
reflection experiments, 144 
sea echoes, 197 

wave propagation over land, 52-58 
wave propagation over the sea, 47-52, 
54-56 

Bulbs (meteorological instruments), 97- 
98 

California Institute of Technology, ane- 
mometer, 100 

Centimeter wave propagation, over- 
land, 52-58 

see also Radio wave transmission 
correlation between theory and ob- 
servations, 54-56 
diurnal signal variations, 53-54 
effect of water vapor in atmosphere, 
53-54 

field strengths, 56-58 
seasonal signal variations, 53-54 
Centimeter wave propagation, oversea, 
47-52, 54-56 


see also Radio wave transmission 
effect of temperature, 56 
light beam behavior, 49 
meteorological factors, 50-52 
monitoring equipment, 56 
observations at variance with theorv, 
54-55 

optical vs nonoptical paths, 50-51 
research recommendations, 54-55 
S-band operation, 48-52 
mtes for experimental stations, 48 , 
soundings as guide to signal varia- 
tions, 54 

transmission paths, 48 
X-band operation, 48-52 
Climate of the West Indies, 39-40 
Clouds, attenuation of radio waves, 160 
Clutter, radar, 201 

Desert temperature, diurnal variation, 
29-32 

Dielectric constant 
fresh water pond, 141 
ground, grass covered, 143 
ground, sandy, 139, 143 
ground, saturated, 141 
ice, 184 

liquid water, 180-185 
sea water, 141 
steam, 185-186 
tap water, 141 

water, temperature variations, 156, 
183-184 

water vapor, 185 

Dielectric constant, measurement 
methods 

reflection-transmission methods, 180 
resonator Q method, 182 
standing wave ratio method, 181 
Diurnal variations in radio transmis- 
sion, 29-32, 50, 53-54 
Dry adiabatic lapse rate, definition, 
132-133 

Dry sandy ground, reflection coeffici- 
ents, 139 
Ducts, 118-128 

see also Ocean ducts, radio trans- 
mission in 

computed climatological informa- 
tion, 126-128 

determination of width, 123-125 
factors affecting extent of trapping, 
123 

modification of air by sea surface, 124 
pressure, temperature, and humidity, 
119-120 

refractive index, 120-123 
Ducts in the trade wind regions, 38-43, 
93-96 

definition, 94 
elevated ducts, 94-95 
frequency of occurrence, 95 


223 


224 


INDEX 


height of duct base, 94-95 
intensity of ducts, 95 
leeward vs windward conditions, 38, 
42 

near the western coasts of continents, 
95-96 

refractive index, 40-43 
surface ducts, 40, 95-96 
thickness of ducts, 95 
vapor pressure difference, 95 
wind speed, 41-43, 95 

Echoes and targets, 191-204 
effect of receiver parameters on signal 
threshold power, 197-202 
fluctuations of radar echoes, 191-195 
frequency dependence of sea echoes, 

195- 197 

radar scattering over cross-section 
area, 202-204 

Electrical constants, 138-144 
dry sandy ground, 139 
for 9 cm waves, 143 
saturated ground, 140 
sea water, 141 

Electromagnetic waves, absorption and 
scattering by dielectric spheres, 
150-154 

Fading in line-of-sight, 58-59 
Fog 

attenuation of radio waves, 160 
effect on radio transmission, 58 
effect on S-band transmission, 50 
Forecasting radio performance from 
meteorological data 
see Meteorology for forecasting radio 
performance 
Formulas 

angle-of-arrival, 207-208 
atmospheric absor})tion and scatter- 
ing, 150-174 

dielectric constants, 181-185 
diffusion equation, 63-65 
electrical constants, 139 
frequency dependence of sea echo, 

196- 197 

gravitational waves, 92 
humidity, relative and specific, 132 
probability that given signal from 
given target will be of given in- 
tensity, 192 

reflection of electromagnetic waves, 
139 

refractive index, 73-78, 89 
refractive index, modified, 132, 138 
signal power dependence on receiver 
parameters, 197-198 
temperature gradient, 59 
Fresnel formulas for reflection of elec- 
tromagnetic waves, 139 
Friez Cycloray recorder, 104 
Front, definition, 132 

Gas absori^tion of radio waves, 148-151, 
171 

Grass-covered ground 
dielectric constant, 143 


reflection coefficients, 142 
Gravitational waves, 92-93 
Gregory humidiometer, 98 
Ground clutter, radar, 193-195 
Ground surfaces, effect on reflection, 146 

Hoyle’s hypothesis, temperature lapse 
rate, 29 

HRK (high sited K-band) receiver, 12 
Humidiometer, 98 

Humidity, effect on nonstandard propa- 
gation, 120 

Humidity measurements, equipment, 
97-98 

Humidity terms (definition), 132 

Ice, dielectric constants, 184 
Index of refraction 

see Refractive index and M curves . 
Irish Sea transmission measurements, 
47-52 

K-band transmission 
attenuation measurement apparatus, 
178 

dielectric constant of steam, 185-186 
HRK receiver, 12 
rain absorption, 160-161 
raindrop attenuation, 148, 158, 164, 
177-180 
receivers, 5 
sea echo, 196 

water vapor absorption, 175-177 
Kite sondes, captive, 104-106 

Leeds and Northrup Speedomax, 104 
Line-of-sight fading, 58-59 
Liquid water, dielectric constant, ISO- 
184 

M (modified refractive index) curves 
see Refractive index and M curves 
Massachusetts Bay radio wave trans- 
mission experiments, 3-18 
Maximum range, radar transmission, 12 
Meteorology 

air flowing over water, 66-67 
diffusion, low-level, 65-66 
diffusion equation, 63 
equilibrium, 67-69 

gravitational waves and temperature 
inversions, 92-93 

refractive index, diurnal variation, 
89-90 

refractive index, fluctuations near 
land or sea, 90-92 
refractive index deficit, 67 
inversion surface, 71-73 
inversions, high, 69-71 
temi)erature and moisture distribu- 
tion, 107-109 

warm air modification by a cold 
water surface, 63-65 
Meteorology, measuring equipment, 
97-106 

anemometers, 99-100 
automatic recording of soundings, 
104-106 


bulbs, wet and dry, 97-98 
captive balloon sondes and kites, 101- 
104 

circuit design for resistor elements, 
98-99 

measurements on board planes and 
dirigibles, 101 
psychrographs, 7 

semipermanent installations, 100-101 
sling psychrometer, 97 
soundings, synthetic, 14 
tables for computing the modified in- 
dex of refraction, 73-88 
temperature and humidity resistance 
elements, 98 

Meteorology for forecasting radio per- 
formance, 47-60, 107-133 
computed climatological information 
on surface ducts, 126-128 
correlation between theories and ob- 
servations, 54-56 
definition of terms, 130-133 
diurnal signal variations, 50, 53-54 
effect of fogs and fronts, 50 
effect of water vapor, 53-54 
overland propagation measurements, 
52-58 

oversea propagation measurements, 
47-52 

radar propagation, 109-118 
relationshi}) between meteorological 
elements and radar performance, 
123-126 

seasonal signal variations, 50, 53-54 
soundings as guide to signal varia- 
tions, 54 

temperature gradient as forecasting 
basis, 56, 59-60 

Meteorology of ocean ducts, 33-46 
leeward vs windward measurements, 
38, 42 

mean soundings, 41-43 
l)rocedure, 33-39 
refractive index, 40-43 
sea temperatures, 42 
summary, 43 
wind speeds, 41-43 
Microwave transmission 

see Centimeter wave propagation; 
Radio wave transmission 
Mixing ratio, definition, 132 
ML-24A psychrometer, 115, 117 
ML-313/AM psychrometer, 116 
Moisture distribution forecasts, 107-109 

National Physical Laboratory, Great 
Britain 

centimeter wave propagation, 47-60 
reflection coefficient measurements, 
147 

Navy Radio and Sound Laboratory, 
balloon sonde, 102 

Neoprene balloons for meteorological 
observations, 103 
Noise figure, radar receiver, 199 

Ocean ducts, radio transmission in, 
33-46 


INDEX 


225 


conclusions, 45-40 
effect of antenna height, 37-39 
effect of -wind speed on duct height, 
41-43 

experimental procedure, 33-39 
meteorological measuring procedure 
and equipment, 33-35, 38 
refractive index of ducts, 40-43 
One-way transmission, 19-28 
experimental equipment and pro- 
cedure, 19-20 

field strength sections, 23-28 
ray theory of trapping, 20-21, 23 
wave guide theory, 21, 23 
Oi)tical path transmission, 50-51, 58-59 
Oxygen in atmosphere, attenuation of 
radio waves, 180 

Plan position indicator (PPI) 

appearance for various types of prop- 
agation, 11 

l)hotographs of radar coverage, 4, 11 
radar echo recording, 198 
“Plumes,” 197 

Pond water, dielectric constant, 141 
Porton towers, meteorological measure- 
ments, 100 

PPI (plan position indicator) 

appearance for various types of prop- 
agation, 111 

])hotographs of radar coverage, 4, 11 
radar echo recording, 198 
Psychrographs, 7 
Psychrometer 

humidity measurements, 97 
radar propagation forecasting use, 
116 

Psychrometric nomogram, 131-133 

Race Point meteorological station, pro- 
cedures, 5 

Radar 

absorption coefficient, 148 
artificial echo, 198 
back scattering, 167-171 
clutter, 201 
displays, 198 
l)ulse repetition rate, 201 
range, maximum, 198 
range, prediction, 123, 125-126 
receiver saturation, 202 
response curve of receiver, 201 
scanning, 200-201 

scattering over cross-section area, 
202-204 

signal detection, 200 
signal fluctuations, 201 
signal threshold power, 198 
storm detection, 187-190 
sweep integration, 200 
target speed, 202 
Watson effect, 202 
Radar echoes, fluctuations, 191-195 
effect of tide, 195 
effect of wind, 191 
pound clutter, 193-195 
intensity of cloud echoes, 192 
interferences, 191 


random scatterers, 192 
targets viewed over water, 195 
Radar ])erformance, effect of meteoro- 
logical conditions, 123-126 
determination of duct width, 123-125 
forecasting of radio and radar ranges, 
123 

qualitative prediction of radar ranges, 
125-126 

summary, 118 ^ 

Radar propagation forecasting, 109- 
118, 123 

see also Meteorology for forecasting 
radio performance 
free balloon flights, 113 
M curves, 111-112 
objectives, 109 
over land, 114-117 
over water, 112-113 
j)lan position indicator, 111 
psychrometer equipment, 116 
range measurements, 112 
recommendations, 117-118 
sounding stations. 111 
WSC wired sonde, 117 
Radar transmission 

see also Radio wave transmission 
correlation with one-way transmis- 
sion, 12-13 

effect of substandard weather condi- 
tions, 13 

in low-lying ocean ducts, 43-46 
maximum ranges, 12 
over- water path measurements, 13-18 
statistics, 12 

target signal strengths, 11-13 
Radiation Laboratory 

captive balloon sondes, 102-103 
reflection coefficient measurements, 
137 

temperature-sensitive resistors, 99, 
101 

Radio meteorology 

see Meteorology for forecasting radio . 
performance 

Radio ranges, prediction, 123 
Radio wave transmission 

see also Centimeter wave propaga- 
tion; Meteorology for forecast- 
ing radio performance 
absorption and scattering by the at- 
mosphere, 148-186 
angle-of-arrival, 205-212 
correlation between calculations and 
measurements, 26-28 
earth constants in microwave range, 
138-147 

echoes and targets, 191-204 
effect of air passing over water, 66-67 
effect of ducts on signal strengths, 
14-17 

effect of nocturnal temperature in- 
versions, 29-32 

experimental equipment and pro- 
cedure, 3-7 

fading in line-of-sight, 58-59 
field strength sections, 23-28 
in low-lying ocean ducts, 43-46 


meteorological measurements, 5-7, 
97-106 

one way, 13-18, 20-28 
optical path transmission, 50-51, 
58-59 

over-water path characteristics, 13-18 
rad^r transmission, 11-13 
ray theory of trapping, 20-21,23 
■ reflection coefficients, 137-147 
reflection theory, 21-23, 26 
refractive index, 10-11, 13-18 
seasonal changes, 9 
signal strength, high vs low receivers, 
10-11 

signal types, 7-9 

storm detection by radar, 187-190 
wave guide theory and trapping, 21, 
23 

Radio wave transmission experiments, 
locale 

Antigua, West Indies, 33-46 
Arizona, 29-32 
England, 47-60 
Irish Sea, 47-52 
Massachusetts Bay, 3-18 
San Diego and Los Angeles, 19-28 
Radio-meteorology 

see Meteorology for forecasting radio 
performance 

Radiosonde recorders, 104-106 
amplifier output reduction, 106 
cable error, 105 
design considerations, 104 
electrical characteristics of elements, 
104-105 

electronic amplifiers, 105-106 
Radiosondes, 101-102 
Rain 

absorption cross section, 157 
attenuation of radio waves, 149, 157- 
159, 162-165 
drop concentration, 161 
drop size, effect on attenuation, 148, 
158-159, 163-164 

drop size distribution in clouds, 160 
echoes on radar, 192 
effect of wavelength on attenuation, 
149 

effect on angle-of-arrival, 206 
effect on radio wave transmission, 46 
K-band attenuation, 177-180 
particle attenuation factor, 154 
precipitation rates, 161-162 
scattering of microwaves, 165-167 
terminal velocity, 161 
Rainfall detection with radar, 188 
Random scatterers, radar, 192 
Ray diagrams for radio wave trans- 
mission analysis, 26-28 
Rav theory of radio wave travel, 20-21, 
23 

Receiver, HRK (high sited K-band), 12 
Recorders for meteorological soundings, 
104-106 

amplifier output reduction, 106 

cable error, 105 

design considerations, 104 


226 


INDEX 


electrical characteristics of elenieiits, 
104-105 

electronic amplifiers, 105-106 
Reflection coefficient, 137-147 

calculation by ray diagrams, 26-28 
correlation with angle-of-arrival, 206 
dependence on thickness of wave- 
length, 21-22 
fresh water pond, 141 
grass-covered ground, 142 
index of refraction, 22-23 
land at centimeter wavelengths, 147 
phase angle shift, 144 
saturated ground, 140 
S-band transmission, 137-147 
sea and land experiments, 144 
sea water, 141 

specular reflection and scattering, 
146-147 
tap water, 141 
vegetation, 142, 147 
very dry sandy ground, 139 
Reflection-transmission method of de- 
termining dielectric constant, 180 
Refractive index and M curves 
correlation with height of antennas, 
17-18, 32 

correlation with 117 me radio trans- 
mission, 14-18 
deficit, 67 
definitions, 130-132 
diurnal variation, 89-90 
effect of temperature inversion, 29-32 
effect on electromagnetic waves, 120 
fluctuations near land or sea, 90-92 
forecasting, 111-112 
in radio wave transmission, 22-23 
isopleths, 72 
M curve, 121-123 

M curve variations and radio signal 
strengths, 10 

M curve versus wind speed, 42-43 
M formula, 132 

meteorological measurements for 
computation of M, 5 
modified index B, 17 
of ocean ducts, 40-43, 120-123 
psychrometric nomograms, 132 
surface trapping, 122 
Refractive index and M curves, tables 
for computing, 73-88 
constants of formula, 77 
formula, 73 

mixing ratio and temperature, 74-77, 
84-88 

pressure versus height, 77 
relative humidity and temperature, 
74-76, 78-83 
use of tables, 74-75 
vapor pressure and temperature, 74 
Relative humidity, definition, 132 
Research recommendations for fore- 
casting radio performance from 
meteorological data, 54-55, 117- 
118 

Resistors, temperature sensitive, 98 
Rye towers, meteorological measure- 
ments, 100 


Sanborn ceramic resistance element, 98 
San Diego radio wave transmission ex- 
periments, 19-28, 69-73 
Saturated ground, reflection coeffici- 
ents, 140 

S-band transmission 
absorption, 147 
antennas, 33-34 

dielectric constant of steam, 185-188 
meteorological factors, 50-52 
radar echoes, fluctuations, 191 
radar echoes from snow, 189 
rain attenuation, 148, 165, 180 
random scatterers, 192 
receivers, 5, 34 

reflection coefficients, 137-147 
sea echo, 196 
signal strengths, 9-11 
signal types, 7-9 
transmitters, 4 

S-band transmission in ocean ducts, 
33-46 

characteristics of ocean ducts, 39-43 
effect of antenna height, 37-39, 44-45 
effect of antenna location, 37-38 
experimental procedure, 33-39 
summary, 43-46 
Scanning rate, radar, 200 
Scattering by the atmosphere 

see Atmospheric absorption and scat- 
tering 

Scattering cross section of spherical 
water drops, 166 
Sea echoes, 195-197 
calm sea, 196 
cause, 195, 197 
effect of Avavelength, 196 
plumes, 197 
stormy sea, 196 
video frequency spectrum, 193 
Sea surface, effect on air, 124 
Sea temperature in West Indies, 40, 42 
Sea water, reflection coefficients, 141 
Seasonal variations in radio transmis- 
sion, 9, 50, 53-54 

Signal threshold power, radar, 198-201 
factors affecting, 199 
measurements, 198 
noise figure, 199 
pulse repetition rate, 201 
radio frequency bandwidth, 199 
sweep speed of scope, 199-200 
video bandwidth, 199 
Sling psychrometer, 97 
Snow attenuation of radio waves, 165 
Snow detection by radar, 189 
Soil temperature, diurnal- variation, 
29-32 

Sondes, captive balloon, 101-104 
cable and balloon technique, 103-104 
radio transmission type, 101-102 
wired transmission type, 102-103 
Sounding equipment for meteorological 
observations, 5, 34-42, 101-104 
Specific humidity, definition, 132 
Specular reflection, 146, 147 
Speedomax, Leeds and Northruj), 104 


Si)herical i)articles, scattering and ab- 
sorj)tion of radio waves, 150-154 
Si)herical raindrops 

attenuation of radio waves, 157-159 
effect of size on scattering, 166 
scattering cross sections, 166 
scattering of microwaves, 165-167 
Standard atmosphere, definition, 130 
Standing Avave ratio method of deter- 
mining dielectric constant, 181 
Steam, dielectric constant, 185-186 
Storm detection by radar, 187-190 
best frequency, 188 
correlation of echoes Avith Av^eather 
conditions, 187-188 
fraction of rainfall detected, 188 
l^rocedures, 187 
range, 189 

S-band echoes from snoAV, 189 
AA-eather information facilities, 187 
Subsidence, definition, 133 

Target speed, effect on radar signal de- 
tection, 202 
Temperature 

effect on duct formation, 119-120 
. effect on nonstandard ranges,’ 59-60 
forecasts, 107-109 

gradient as basis for radio jAerform- 
ance forecasting, 56, 59-60 
“AV’et bulb” temperature, 132 
Temperature inversions 
characteristics, 89 

effect on one-Avay radio tranmission, 
20-21 

effect on radio Avave refraction index, 
29-32 

meteorological analysis, 92-93 
Temi)erature-sensitive resistors, 98 
Thermometers, Avet and dry bulbs, 97 
Trade Avand areas, meteorology 
see Ducts in the trade Avind regions 
Transmitters for use in radio transmis- 
sion experiments, 3-4, 19 
Trapping of radio AA^aves, 20-26 
ray theory, 20-21 
reflection theory, 21-23 
summary, 23-26 
AA'ave guide theory, 21 

Ultra Short Wave Proi)agation Panel, 47 

Vapor pressure gradients, 89 
Vegetation, effect on reflection, 142, 147 
Video bandAvidth, radar, 199 

Washington State College, temi)era- 
ture-sensitive resistors, 98, 101 
Water, dielectric constant, 156 
Water vapor 

attenuation coefficient, 177 
attenuation of radio waves, 185 
effect on overland radio transmission, 
53-54 

Watson effect, radar, 202 
Wave guide theory of radio Avave travel, 
21 

Weather, substandard, effect on radar 
transmission, 13 


INDEX 


227 


^^'est Indies, climate survey, 39-40 
^^'et and dry bulb thermometers for 
humidity measurements, 97-98 
Wet bulb temperature, definition, 132 
Wind speed 

effect on diurnal temperature varia- 
tions, 30 

effect on ground clutter, 193-194 
in ocean ducts, 40-43, 95 
in West Indies, 40-43 
measuring equipment, 99-100 
Window, 192 


WSC wired sonde, use in radar propaga- 
tion forecasting, 117 

X-band transmission 
angle-of-arrival measurements, 209- 
212 

antennas, 33-34 

dielectric constant of steam, 185-186 
radar echoes, fluctuations, 191 
rain attenuation, 148, 164, 180 / 

random scatterers, 192 
receivers, 5, 34 


reflection, 137, 146 
sea echo, 196 
signal strengths, 9-11 
signal types, 7-9 
transmitters, 4 

X-band transmission in ocean ducts 
characteristics of ocean ducts, 39-43 
effect of antenna height, 37-39, 44-45 
effect of antenna location, 37-38 
experimental procedure, 33-39 
summary, 43-46 












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